MATH145 Lecture Notes - Lecture 18: Vr Class Sm1

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X k =1 k m = 1m + 2m + 3m + . For xed n z+, we can nd a recursion formula for. X k =1 k 1 = n(n + 1) X k =1 (k + 1)m+1 k m+1 n. X k =0 (k + 1)m+1 k m+1 = (n + 1)m+1 (k + 1)m+1 k m+1 ((k m+1 + (cid:16)m + 1. 2 (cid:17)k m 1 + + (cid:16)m + 1 m (cid:17)k + (cid:16)m + 1 m + 1(cid:17)) k m+1) 2 (cid:17) k m + (cid:16)m + 1. X k =0 k m 1 + + (cid:16)m + 1 m (cid:17) k m 1 + + (cid:16)m + 1 m (cid:17) k + (cid:16)m + 1 m + 1(cid:17) n. 1 m + 1 ((n + 1)m+1 (cid:16)m + 1. 2 (cid:17)sm 1 (cid:16)m + 1 m (cid:17)s1 s0 1)

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