Solution Found!
Show that, if c is a positive real number, then g(n) = 1 + c + c2 + + cn is:(a) (1) if c
Chapter 0, Problem 0.2(choose chapter or problem)
Show that, if is a positive real number, then g(n) = 1 + c + c2 + … + cn is:
(a) Θ(1) If c < 1.
(b) Θ(n) If c = 1.
(c) Θ(cn) If c > 1.
The moral: in big-Θ terms, the sum of a geometric series is simply the first term if the series is strictly decreasing, the last term if the series is strictly increasing, or the number of terms if the series is unchanging.
Questions & Answers
QUESTION:
Show that, if is a positive real number, then g(n) = 1 + c + c2 + … + cn is:
(a) Θ(1) If c < 1.
(b) Θ(n) If c = 1.
(c) Θ(cn) If c > 1.
The moral: in big-Θ terms, the sum of a geometric series is simply the first term if the series is strictly decreasing, the last term if the series is strictly increasing, or the number of terms if the series is unchanging.
ANSWER:Step 1 of 4
The geometric series given is 
* First term, if the series is strictly decreasing.
* Last term, if the series is strictly decreasing.
* The number of terms, if the series is unchanging.