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
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-> 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
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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.
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For the general case of any geometric progression, the proof for its sum by the method of mathematical induction is in the lesson
