SOLUTION: Let P(n) be the statement that 3^1 + 3^2 + � � � 3^n = 3/2(3^n-1) for the positive integer n. A proof by mathematical induction is to be used to establish this summation formula

Question 1123974: Let P(n) be the statement that
3^1 + 3^2 + � � � 3^n = 3/2(3^n-1)
for the positive integer n. A proof by mathematical induction is to be used to establish this
summation formula.
(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.

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
For the general case of any geometric progression, the proof for its sum by the method of mathematical induction is in the lesson

https://www.algebra.com/algebra/homework/Sequences-and-series/Mathematical-induction-and-geometric-progressions.lesson

https://www.algebra.com/algebra/homework/Sequences-and-series/Mathematical-induction-and-geometric-progressions.lesson

in this site.

RELATED QUESTIONS
use mathematical induction to prove that the following statement is true for every... (answered by ikleyn)

use mathematical induction to prove that the following statement is true for every... (answered by ikleyn)

Prove that n^3 + (n+1)^3 + (n+2)^3 is divisible by 9 for all n in Natural numbers. I... (answered by aaaaaaaa,mathslover)

Identify the correct proof by induction or a counterexample to disprove the following... (answered by ikleyn,Edwin McCravy)

Use mathematical induction to prove the statement is true for all positive integers n. (answered by Edwin McCravy)

Prove by mathematical induction,1^2+3^2+....(2n+1)^2=((n+1)(2n+1)(2n+3))/3 where 'n' is a (answered by ikleyn)

proof this statement using math induction :... (answered by Edwin McCravy,ikleyn)

Identify the correct base case for a proof by induction for the following statement.... (answered by richard1234)

Use mathematical induction to prove the statement is true for all positive integers n. (answered by ikleyn)