Use mathematical induction to prove the formula for all integersnz 1. 6 + 12 + 18 + 24 + ... + 6n = 3n(n + 1) Find S, when n = 1. Your answer cannot be understood or graded. More Inform. Enter an exact number. Assume that S, = 6 + 12 + 18 + 24 + ... + 6k = 3k(k + 1). Then, Sk+1 Sk + ak + 1 = (6 + 12 + 18 + 24 + ... + 6k) + ak + 1 ak +1= Use the equation for ak+ 1 and S, to find the equation for S+1: Sk+1= Is this formula valid for all positive integer values of n?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Use mathematical induction to prove the formula for all integersnz 1.
6 + 12 + 18 + 24 + ... + 6n = 3n(n + 1)
Find S, when n = 1.
Your answer cannot be understood or graded. More Inform.
Enter an exact number.
Assume that
S, = 6 + 12 + 18 + 24 + ... + 6k = 3k(k + 1).
Then,
Sk+1
Sk + ak + 1 = (6 + 12 + 18 + 24 +
... + 6k) + ak + 1
ak +1=
Use the equation for ak+ 1
and S, to find the equation for S+1:
Sk+1=
Is this formula valid for all positive integer values of n?
Transcribed Image Text:Use mathematical induction to prove the formula for all integersnz 1. 6 + 12 + 18 + 24 + ... + 6n = 3n(n + 1) Find S, when n = 1. Your answer cannot be understood or graded. More Inform. Enter an exact number. Assume that S, = 6 + 12 + 18 + 24 + ... + 6k = 3k(k + 1). Then, Sk+1 Sk + ak + 1 = (6 + 12 + 18 + 24 + ... + 6k) + ak + 1 ak +1= Use the equation for ak+ 1 and S, to find the equation for S+1: Sk+1= Is this formula valid for all positive integer values of n?
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