Home
Class 12
MATHS
If sum of the mth powers of first n odd ...

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)`

Text Solution

Verified by Experts

The correct Answer is:
D
`:.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)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the sum of first n even numbers.

Find the sum of first n odd natural numbers.

The sum of all two digit odd numbers is :

Prove that the sum of two odd numbers is even.

If the sum of first n odd natural number is 1225, find the value of n.

Let S_(n) denote the sum of the cubes of the first n natural numbers and s_(n) denote the sum of the first n natural numbers. Then sum_(r=1)^(n)(S_(r))/( S_(r )) equals :

Find the sum of first n even natural numbers.

Express 49 as the sum of 7 odd numbers

The variance of the first n natural numbers is :

Statement 1 The difference between the sum of the first 100 even natural numbers and the sum of the first 100 odd natural numbers is 100. Statement 2 The difference between the sum of the first n even natural numbers and sum of the first n odd natural numbers is n.