Question: Prove the following problem using mathematical induction. 1*2*3 + 2*3*4 + ... + n(n + 1)(n + 2) = n(n + 1)(n + 2)(n +

Prove the following problem using mathematical induction. 1*2*3 + 2*3*4 +

Prove the following problem using mathematical induction. 1*2*3 + 2*3*4 + ... + n(n + 1)(n + 2) = n(n + 1)(n + 2)(n + 3)/4Prove for n> = l Sigma_k = 1^n k(k + 1)(k + 2) = n(n + 1)(n + 2)(n + 3)/4 IMPORTANT: when filling in the blanks, be sure to put things in ascending order. YES n(n+1)(n+2)... NO ...(n+2)(n+1)n Basis: n = 1 A. Sigma_k = _____^_____ _____ (_______)(_______) = ___________ B. ______(_______) (_______)(_______)/4 = ________ Does A - B? (y) ________ Assume: Sigma_k = ___^________ _______(_______) (_______) = (_______)(_______)(_______)(_______)/4 Prove: sigma_k = _______^______ _________ (_______)(_______) = (_______)(_______)(_______)/4 sigma_k = _______^______ ___________ (_______)(_______) = sigma_k = ______^_____ ______(_______) (_______) + (_______)(_______)(_______) = __________ (_______)(_______)(_______)/4 + (_______)(_______)(_______) = (_______)(_______)(_______)(_______) + 4(_______)(_______)(_______)/4

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