Question

Use mathematical induction to prove that: \[ 2(3)+2(3)^{2}+\cdots+2(3)^{n-1}=3^{n}-3 \] for all positive integers

          Use mathematical induction to prove that:
\[
2(3)+2(3)^{2}+\cdots+2(3)^{n-1}=3^{n}-3
\]
for all positive integers

Use mathematical induction to prove that:

2(3)+2(3)^2+⋯+2(3)^n-1=3^n-3

for all positive integers

Added by Jeffery N.

Precalculus

Ron Larson 10th Edition

Chapter 9

Instant Answer

Solved by Expert Linda Hand

06/07/2021

Step 1

When n = 1, the left-hand side of the equation becomes: \[2(3)^{1-1} = 2(1) = 2\] And the right-hand side of the equation becomes: \[3^{1} - 3 = 3 - 3 = 0\] Since 2 is not equal to 0, the equation does not hold true for n = 1. Show more…

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Question

Use mathematical induction to prove that: \[ 2(3)+2(3)^{2}+\cdots+2(3)^{n-1}=3^{n}-3 \] for all positive integers

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