SUM the following series, with every other successive denominator in the bracket being greater than the previous one by "1" ?

1/3[(1/2-1/5)+(1/3-1/6)+(1/4-1/7)+....]

1 Answer
Jul 28, 2018

13/36

Explanation:

first of all, divide the sum into to parts- the positive constants and the negative constants.
=1/3{[1/2+1/3+1/4+1/5+......]-[1/5+1/6+1/7+......]}
cancel the constants of opposite signs,i.e., from 1/5 to infinity.
=1/3{1/2+1/3+1/4}
take LCM on the inside
=1/3{[6+4+3]/12}
=13/36

hope this helps,
Shivang M.