(a) Note how ni=1 i3 + (n + l)3 = ni=0 (i + 1)3 = ni=0 (i3...

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(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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