Question: (a) Note how ni=1 i3 + (n + l)3 = ni=0 (i + 1)3 = ni=0 (i3 + 3i + 1). Use this result to

(a) Note how ∑ni=1 i3 + (n + l)3 = ∑ni=0 (i + 1)3 = ∑ni=0 (i3 + 3i + 1). Use this result to obtain a formula for ∑ni=1 i2. (Compare with the formula given in Example 4.4.)
(b) Use the idea presented in part (a) to find a formula for ∑ni=1 i3 and one for ∑ni=1 i4. [Compare the result for ∑ni=1 i3 with the formula in part (d) of Exercise 1 for this section.]

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a From n i1 i 3 n 1 3 n i0 i 3 3i 2 3i 1 n i1 i 3 3 n i1 i 2 3 n i1 i 2 3 n i1 i n i0 1 we have n l ... View full answer

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