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Subtract the correct prefix from a finite sum

Given ∑r=0n1/[(r+1)(r+2)(r+3)]=14−1/[2(n+2)(n+3)]\sum_{r=0}^n1/[(r+1)(r+2)(r+3)]=\tfrac14-1/[2(n+2)(n+3)], deduce ∑r=5201/[(r+1)(r+2)(r+3)]\sum_{r=5}^{20}1/[(r+1)(r+2)(r+3)]. marks

[2010/MI/Promo/5(modified)]

CJC · Review problems · Question 4

The unwanted prefix ends at 4 because the retained first index is 5.

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