SOLUTION: Find the following sum . (2) {{{ Sn=1/(1*3) + 1/(2*4) + 1/(3*5) +...}}}{{{1/n(n+2)}}}

Algebra ->  Sequences-and-series -> SOLUTION: Find the following sum . (2) {{{ Sn=1/(1*3) + 1/(2*4) + 1/(3*5) +...}}}{{{1/n(n+2)}}}      Log On


   

Question 1054643: Find the following sum .
(2) +Sn=1%2F%281%2A3%29+%2B+1%2F%282%2A4%29+%2B+1%2F%283%2A5%29+%2B...1%2Fn%28n%2B2%29
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Notice that for the general term 1%2F%28k%2A%28k%2B2%29%29 = %281%2F2%29%2A%281%2Fk-1%2F%28k%2B2%29%29.

Therefore, when you apply this formula to every term of your series, many (most !) fractions will be canceled.

Only few will survive. This is an idea.