Find the sum of series`(3^3=2^3)+(5^3=4^3)+(7^3=6^3)+`to `n`terms

1.	Find the sum of series`(3^3=2^3)+(5^3=4^3)+(7^3=6^3)+`to `n`terms
Answer» We have `T_(k)={(2k+1)^(3)-(2k)^(3)}` `={8k^(3)+1+6k(2k+1)-8k^(3)}=(12k^(2)+6k+1).` (i) sum to n terms is given by `S_(n) =12 sum_(k=1)^(n)k^(2)+6sum_(k=1)^(n)k+n` `=12xx(1)/(6)n(n+1)(2n+1)+6xx(1)/(2)n(n+1)+n` `=2n(n+1)(2n+1)+3n(n+1)+n` `=n(n+1)[4n+2+3]+n=n[(n+1)(4n+5)+1]` `=n(4n^(2)+9n+6)=(4n^(3)+9n^(2)+6n).` (ii) Sum to 10 terms is given by `S_(10) =10 xx[4 xx10^(2)+9xx10+6]=4960.`

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