Find the sum of the series `(1^3)/1+(1^3+2^3)/(1+3)+(1^3+2^3+3^3)/(1+3+5)+` up to `n` terms.

Explanation

`r^(th)` term in the given expression can be given as,

`T_r = (1^3+2^3+3^3+...)/(1+3+5+...)`

`=>T_r = (((r(r+1)))/2)^2/(r^2)`

`=>T_r = (r^2(r+1)^2)/(4r^2)`

`=>T_r = 1/4(r+1)^2`

`=>T_r = 1/4(r^2+1+2r)`

`:.` Sum of given series ` = sum T_n = 1/4 (sum n^2+ sum 1 + sum 2n)`

`= 1/4[(n(n+1)(n+2))/6+n+2*(n(n+1))/2]`

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