SOLUTION: Solve 1 power 4/ (1 x 3) + 2 power 4 /(3 x 5) +3 power 4/(5 x 7)………………n power 4/(2n-1)(2n+1)

Algebra ->  Sequences-and-series -> SOLUTION: Solve 1 power 4/ (1 x 3) + 2 power 4 /(3 x 5) +3 power 4/(5 x 7)………………n power 4/(2n-1)(2n+1)       Log On


   

Question 931537: Solve 1 power 4/ (1 x 3) + 2 power 4 /(3 x 5) +3 power 4/(5 x 7)………………n power 4/(2n-1)(2n+1)




Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
1 power 4/ (1 x 3) + 2 power 4 /(3 x 5) +3 power 4/(5 x 7)………………n power 4/(2n-1)(2n+1) 
sum%28k%5E4%2F%28%282k-1%29%282k%2B1%29%29%2Ck=1%2Cn%29

We break k%5E4%2F%28%282k-1%29%282k%2B1%29%29

into partial fractions, first by writing it as 

Then break 1%2F%28%282k-1%29%282k%2B1%29%29 into partial fractions, getting

expr%281%2F2%29%281%2F%282k-1%29-1%2F%282k%2B2%29%29

Then that's telescoping series.  Then use the sum of squares formula

and put it altogether and you end up with the expression for the sum as

%28n%28n%5E3%2B2n%5E2%2B2n%2B1%29%29%2F%286%282n%2B1%29%29

Edwin