Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 11838 by Peter last updated on 02/Apr/17

((2^2 +1)/(2^2 −1)) + ((3^2 +1)/(3^2 −1)) + ((4^2 +1)/(4^2 −1)) + .... + ((20^2 +1)/(20^2 −1)) = ....?

22+122−1+32+132−1+42+142−1+....+202+1202−1=....?

Answered by ajfour last updated on 02/Apr/17

T_r = ((r^2 +1)/(r^2 −1)) = ((r^2 −1+2)/(r^2 −1)) =1+(2/((r−1)(r+1))) T_r = 1+(1/((r−1)))−(1/((r+1))) S= Σ_(r=2) ^(r=20) T_r = (1+(1/1)−(1/3)) +( 1+(1/2)−(1/4)) +(1+(1/3)−(1/5)) + (1+(1/4)−(1/6)) +.... ...+(1+(1/(17))−(1/(19))) +(1+(1/(18))−(1/(20))) +(1+(1/(19))−(1/(21))) S = 19+1+(1/2)−(1/(20))−(1/(21)) S= 20+((169)/(420)) .

Tr=r2+1r2−1=r2−1+2r2−1=1+2(r−1)(r+1)Tr=1+1(r−1)−1(r+1)S=∑r=20r=2Tr=(1+11−13)+(1+12−14)+(1+13−15)+(1+14−16)+.......+(1+117−119)+(1+118−120)+(1+119−121)S=19+1+12−120−121S=20+169420.

Terms of Service

Privacy Policy

Contact: info@tinkutara.com