The formula 1 + 2 + 3 ++ n = n(n + 1) 2 is true for all integers n 1. Use this fact to

Chapter 5, Problem 1

(choose chapter or problem)

The formula

\(1+2+3+\cdots+n=\frac{n(n+1)}{2}\)

is true for all integers n ≥ 1. Use this fact to solve each of the following problems:

a. If k is an integer and k ≥ 2, find a formula for the expression 1 + 2 + 3+· · ·+(k − 1).

b. If n is an integer and n ≥ 1, find a formula for the expression 3 + 2 + 4 + 6 + 8+· · ·+2n.

c. If n is an integer and n ≥ 1, find a formula for the expression 3 + 3·2 + 3·3+· · ·+3·n + n.

Text Transcription:

1+2+3+ cdots+n= n(n+1) / 2