Use mathematical induction to prove the formula for all integers n 2 1. 12 + 22 + 32 + 4² + …. + n 2 _ n(n + 1)(2n + 1) Find S, when n = 1. Assume that S = 12 + 22 + 3² + 4² + ... + k? = k(k + 1)(2k + 1) 6 Then, ... + k²) + ak + 1' Sk +1 = Sk + ak + 1 = (1² + 2² + 32 + 4² ak +1= Use the equation for a+1 and S, to find the equation for SK + 1' Sk+1
Use mathematical induction to prove the formula for all integers n 2 1. 12 + 22 + 32 + 4² + …. + n 2 _ n(n + 1)(2n + 1) Find S, when n = 1. Assume that S = 12 + 22 + 3² + 4² + ... + k? = k(k + 1)(2k + 1) 6 Then, ... + k²) + ak + 1' Sk +1 = Sk + ak + 1 = (1² + 2² + 32 + 4² ak +1= Use the equation for a+1 and S, to find the equation for SK + 1' Sk+1
Chapter8: Sequences, Series,and Probability
Section8.4: Mathematical Induction
Problem 2ECP
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