Question: Let P(n) be the statement that 13 23 33 ... n3 = (n(n 1)2)2 for the positive integer n. Complete the inductive step, identifying where
Let P(n) be the statement that 13 23 33 ... n3 = (n(n 1)2)2 for the positive integer n. Complete the inductive step, identifying where you use the inductive hypothesis. Multiple Choice Replacing the quantity in brackets on the left-hand side of part (c) by what it equals by virtue of the inductive hypothesis, we have (k(k 1)2)2 (k 1)3=(k 1)3(k2 4k 14)=((k 1)(k 2)2)2 as desired. Replacing the quantity in brackets on the left-hand side of part (c) by what it equals by virtue of the inductive hypothesis, we have (k(k 1)2)2 (k 1)3=(k 1)2(k2 4k 44)=((k 1)(k 2)2)2 as desired. Replacing the quantity in brackets on the left-hand side of part (c) by what it equals by virtue of the inductive hypothesis, we have (k(k 1)2)2 (k 1)2=(k 1)2(k2 4k 14)=((k 1)(k 2)4)2 as desired. Replacing the quantity in brackets on the left-hand side of part (c) by what it equals by virtue of the inductive hypothesis, we have (k(k 1)2)3 (k 1)2=(k 1)2(k2 4k 44)2=((k 1)(k 2)4)2 as desired
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