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Bob J.

asked • 02/05/16

Prove Statement using the First Principle of Mathematical Induction

Prove the following statements using the First Principle of Mathematical Induction:

(a) If r ≠ 1, then

1 + r + r2 + ... + rn = (1 − rn+1)/(1-r)


for all n ∈ N. Why does the formula not work when r = 1?, what will be the “formula” for 1 + r + r2 + ... + rn when r = 1?

(b) For all n ∈ N with n ≥ 2,

3n > 3n + 1.

Is the previous result true for n = 1?

(c) 5 | (42n − 1) for all n ∈ N.

2 Answers By Expert Tutors

By:

Arnold F. answered • 02/05/16

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5 (53)

College Professor & Expert Tutor In Statistics and Calculus

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