Porisma

A hint to get started

Shift both bounds before applying a prefix formula

Given ∑r=2n−1[2r+4(1/(r+1)−1/r)]=n2−n+4/n−4\sum_{r=2}^{n-1}[2r+4(1/(r+1)-1/r)]=n^2-n+4/n-4, show

∑r=92n−2[2r+2+4(1r+2−1r+1)]=4n2−2n+2n−4525.\sum_{r=9}^{2n-2}\left[2r+2+4\left(\frac1{r+2}-\frac1{r+1}\right)\right]=4n^2-2n+\frac2n-\frac{452}5.
marks

[2013/SRJC/Promo/10(modified)]

CJC · Review problems · Question 7

Use k=r+1 and transform the lower and upper limits along with the summand.

Read the worked solution