Question

Calculation question: (see attachment)

Answer 1

u know the answer? is it 209/4200 ??

Answer 2

whatever be the answer, u can proceed this way and get the answer:
notice that all the terms are in the form:
\[1/5(n-1)n(n+1) \] form
so, u can write it this way:
\[[(1/n-1)-(1/n+1)]/10n\]
take the 1/10 common
so, if a term is 1/r(r-1) - 1/r(r+1), the next term is 1/r(r+1) - 1/(r+1)(r+2)
when adding these two, note that the term 1/r(r+1) gets cancelled
so, proceeding this way, we can get 1/1*2 - 1/20*21 = 209/420
multiply with 1/10, u will get 209/4200

Answer 3

But Arnab09, 1/5(n−1)n(n+1) does not quite tally with the terms for the equation. (n-1) for the first term is zero, and any number multiplied by zero remains zero...

Answer 4

no, here the terms start with n=2

Answer 5

i have taken the middle term as n.. :)

Answer 6

Goodjob arnab

Answer 7

oh! ok, thanx

Answer 8

Now I understand... :)

Answer 9

given series is::
Sn=(summation form n=1 to n=19)(1/5)((1/2r)-(1/r)+1/2(r+1))...expand this equation and you will get :
Sn=(1/5)*(1/4-1/2(n+1)(n+2))....put here n=19
and Sn=209/4200..ans