For each integer n with n 2, let P(n) be the formula n1 i=1 i(i + 1) = n(n 1)(n + 1) 3
Chapter 5, Problem 4(choose chapter or problem)
For each integer n with n ≥ 2, let P(n) be the formula
\(\sum_{i=1}^{n-1} i(i+1)=\frac{n(n-1)(n+1)}{3}\).
a. Write P(2). Is P(2) true?
b. Write P(k).
c. Write P(k + 1).
d. In a proof by mathematical induction that the formula holds for all integers n ≥ 2, what must be shown in the inductive step?
Text Transcription:
sum_i=1^n-1 i(i+1)= n(n-1)(n+1) / 3
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