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Let P(n) be the statement that 12 + 22+ = n(n + 1)(2n+1)6

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 3E Chapter 5.1

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 3E

Let P(n) be the statement that 12 + 22+ = n(n + 1)(2n+1)6 for the positive integer n.a) What is the statement P(1)?________________b) Show that P(1) is true, completing the basis step of the proof.________________c) What is the inductive hypothesis?________________d) What do you need to prove in the inductive step?________________e) Complete the inductive step, identifying where you use the inductive hypothesis.________________f) Explain why these steps show that this formula is true whenever n is a positive integer.

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WEEK NINE 4.4.16 th th Popular US Entertainment: Late 19 /Early 20 Centuries -Shows that appeal to as many people across societal groups as possible for commercial purposes -Sooooo, mostly white males -The Minstrel Show -“Ethnic” musical entertainments: loosely plotted plays with music -Included rapidly shifting scenes, a great diversity of characters you would find in the city at that time, and lots of spectacle (including song and dance) -Tom and Jerry Shows (mocking Irish/Urban) focused on a character called Mose, a fireman from the Bowery played by Frank Chanfrau in a rugged, red flannel with suspenders and jeans and a squished top hat and Irish-black hair -Borrowed from a popular British character -Beginning of “consciously processing local history” -Harrigan, Hart, and Braham (mocking Irish) -The Fritz Shows (German) -Weber and Fields (“Dutch” or Jewish) -All of the above: based on mocking a certain culture -Led to Minstrel Shows; blackface (“blacking” or “corking” up) was popular by 1832 -Thomas Dartmouth Daddy (“TD”) Rice performed in 1830s with his “Jump Jim Crow” character th -It wasn’t until the 1840s-early 20 century that Minstrel Shows became popular as a full night of entertainment (i.e. not an isolated act) -Minstrel Shows are the first uniquely American theatrical form and, worth noting, they weren’t popular in the South (just the North) -Had a large part in how Northerners (mis)understood slavery -Directly linked to Vaudeville, Burlesque, and early American musical comedies -Edwin P. Christy and the Christy Minstrels shaped the art form -Act One: sat in a line with Tambo and Bones on either end (so named for the instruments they played) and Mr. Interlocutor in the middle (not in blackface; considered the “straight man”) -Charlemagne’s line, “gentlemen, be seated” before “War is A Science” in Pippin A blatant reference to minstrel shows, as is that entire number. -First act consists of lots of jokes, banter, etc., and ends with a walk- around -Act Two: called the Fantasia or Olio (reused cooking fat) -Individual specialty numbers (arias, soft-shoes, recitations, etc.); not necessarily comedic buuuut usually full of racially-driven comedy -Lots of cross-dressing (white men in blackface as highly sexualized black women) -Act Three: the Burlesque (which originally means “to parody”) -Parodied a popular cultural event or figure -Black minstrel performers came to exist (though they still had to cork up) -Bizarre paradox, but was at least an opportunity for black performers to gain popularity (!) 4.6.16 Vaudeville (1860s-1930s) -Defined as a show consisting of unrelated acts fthlowing one another in succession -The concept of variety theatre originated in 15 C France in a village called Val de Vire but the US perfected it in the 19 century -Tony Pastor’s Fourteenth Street Theatre -Opens in 1865 for financial reasons (post-war) -Middle class has expendable income; women become target audience -Leads to the need for clean, family-friendly entertainment; no smoking, alcohol, or sexual references -Introduces practical raffles, etc. to keep female/family audiences interested -Benjamin F. Keith (1864-1914) and Edward F. Albee (1870-1930) -No, not that Edward Albee; his grandfather -Formed their own Vaudeville theatre in 1887 and took over their own circuit (the Keith circuit) -Opened using money from a successful G&S theatre they owned in Boston -Keith got old and Albee took over; started charging artists 5% booking fees (a la Syndicate) -United Booking Office (1906) -Albee eventually partnered with Joseph P. Kennedy, a movie guy, and together they turned most Vaudeville houses into movie houses and later became RKO -Standard Nine-Act Bill: 1. Dumb Act (didn’t need to hear; okay to trickle in) 2. Crowd Seller (usually male and female singing duet) 3. Wake up the audience (sketch) 4. Corker (first big punch; some secondary names) 5. Big Act (headliner or dance number) Intermission (put names in for raffles) 6. Famous comedy dumb act 7. Headliner playlet 8. Chief Attraction (major solo headliner) 9. Tech-heavy act (animals, acrobats in elaborate costumes, etc.) -Often had ridiculous four-show days -Types of acts/famous people from/who started in Vaudeville: Houdini, Fanny Brice, The Petomane, The Regurgitator, acrobats/actors/etc., and pretty much every Broadway star of the 20s-40s (including black performers) -Legacy: first cheap, family-friendly entertainment; relatively non-discriminatory (still segregated but anyone could attend); excellent training 4.8.16 Burlesque (1860s-1939) -Didn’t used to be sexy -Plot-based, fully composed parody/spoof -Evangeline (1874) -Originated as an after piece; very popular -Introduced the Heifer Dance (moo-moo moo-moo) -Lydia Thompson and her British Blondes -All female; first burlesque that was more about the clothing than the plot -She was the producer; introduced leg shows -Took New York by storm in 1867 -Michael Leavitt and the Rentz-Santley Shows (1869-1879) -Originator of American Burlesque -Turned the end men of minstrel shows in end-women -Starred Mable Santley -Very little actual burlesquing; replaced by women in tights (no nudity or stripping yet) -Eventually, this became the format: 1. Candy Butcher’s spiel (emcee, basically) 2. Opening chorus number (all female) 3. Monologues, songs, dances, etc. Intermission (now with alcohol!) 4. Another Candy Butcher spiel 5. Specialty number 6. Added Attraction (read: strip tease) 7. Finale -Two main circuits, called wheels (Empire Wheel and Columbia Wheel) -The Burlesque Slump (1890-1900) occurs as morality goes back in style -Audiences became incentivized with contests and amateur nights -Introduced the Hook -Golden Age of Burlesque (1900-1910) -Introduced many of the best Broadway-bound comedians -Strong focus on production value -Men and women in the audience -Burlesque Lingo: -Jerk = Audience Member -Yuck = Laugh -Talking Woman = the straight woman in a comedy routine -“The asbestos is down” = no one is laughing -Mountaineer = someone who just joined in from the catskills -Top banana = highest ranking comic -Blisters = breasts -Cheeks = butt -Gadget = G-string Quiver, shimmy, bump, grind = self-explanatory -Striptease Technique -All about posing, strutting, dancing, and singing, with some bumps and grinds -Originally more about the monologue/tease than the removal of clothing 1. The Flash (pose) 2. The Parade/Trailer (walk and talk) 3. The Tease (clothing starts coming off 4. The Climactic Strip (the final piece of clothing; she’s naked!) 5. The Speedy Retreat -There were only about five seconds of actual nudity in what might’ve been at least a ten- minute act -The Minsky’s (1920-1939) introduced the bump and grind (on floors/objects) -Turned burlesque into stripping -Mayor Fiorello banished the words “burlesque” and “Minsky” (synonymous) -In 1942, the Supreme Court declared burlesque to be “inartistic filth”; makes it illegal -Their burlesque house is now the New Vic Theater! -Factors in the downfall of burlesque: WWII, church/media, prohibition, Great Depression, the unionization of stagehands, litigation, bankruptcy, corruption, and the increasing prevalence of nudity in Broadway Revues

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Chapter 5.1, Problem 3E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

This full solution covers the following key subjects: inductive, show, statement, true, Integer. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Let P(n) be the statement that 12 + 22+ = n(n + 1)(2n+1)6 for the positive integer n.a) What is the statement P(1)?________________b) Show that P(1) is true, completing the basis step of the proof.________________c) What is the inductive hypothesis?________________d) What do you need to prove in the inductive step?________________e) Complete the inductive step, identifying where you use the inductive hypothesis.________________f) Explain why these steps show that this formula is true whenever n is a positive integer.” is broken down into a number of easy to follow steps, and 77 words. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 3E from 5.1 chapter was answered, more than 313 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 3E from chapter: 5.1 was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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Let P(n) be the statement that 12 + 22+ = n(n + 1)(2n+1)6