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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