If sum of the mth powers of first n odd numbers is `lambda,Aamgt1`, then (A)`lambdaltn^(m)` (B)`lambdagtn^(m)` (C)`lambdaltn^(m+1)` (D)`lambdagtn^(m+1)`

Options

A. `lambdaltn^(m)`
B. `lambdagtn^(m)`
C. `lambdaltn^(m+1)`
D. `lambdagtn^(m+1)`

Answer

D

Explanation

`:.mgt1`
`:.(1^(m)+3^(m)+5^(m)+"..."+(2n-1)^(m))/(n)gt((1+3+5+"..."+(2n-1))/(n))^(m)`
`=(((n)/(2)(1+2n-1))/(n))^(m)=n^(m)`
`:.1^(m)+3^(m)+5^(m)+"..."+(2n-1)^(m)gtn^(m+1)`
Hence, `lambdagtn^(m+1)`