Question
Prove the following proposition using induction:
P(n): 1² + 2² + 3² + 4² + ... ... ... ... . + n² = n(n+1)(2n+1) / 6
Answer :
Word Count : 310
For n = 1, the left-hand side is 1² = 1. The right-hand side gives 1(1 + 1)(2·1 + 1) / 6 = 1·2·3 / 6 = 1. Thus the proposition is true for n = 1. Assume that the proposition is true for some positive integer k, that is, 1² + 2² + 3² + … + k² = k(k + _____ ___ ____ ___ ___.
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For n = 1, the left-hand side is 1² = 1. The right-hand side gives 1(1 + 1)(2·1 + 1) / 6 = 1·2·3 / 6 = 1. Thus the proposition is true for n = 1. Assume that the proposition is true for some positive integer k, that is, 1² + 2² + 3² + … + k² = k(k + _____ ___ ____ ___ ___.
_______ _________ _____ _______ ____ ________ ___ ________ __________ _______ __________.
_____ ______ ___ _________ _________.
_________ ______ __________ _________ _____ _____ ______ __________.
_____ _______ ___ ___ ___ ___ _____ ________ __________ ______ ________.
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