Home
Class 12
MATHS
If the value of "^(n)C(0)+2*^(n)C(1)+3*^...

If the value of `"^(n)C_(0)+2*^(n)C_(1)+3*^(n)C_(2)+...+(n+1)*^(n)C_(n)=576`, then `n` is (a) 7 (b) 5 (c) 6 (d) 9

A

`7`

B

`5`

C

`6`

D

`9`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `S=^(n)C_(0)+2.^(n)C_(1)+3.(n)C_(2)+...+(n+1).^(n)C_(n)`
Here `T_(r )=(r+1)^(n)C_(r )=n^(n-1)C_(r-1)+^(n)C_(r )`
`:.S=n^(2n-1)+2^(n)=576` (given)
`:.n=7`
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of (""^(n) C_(1)+2. ""^(n) C_(2)+3. ""^(n)C_(3)+…+ n""^(n)C_(n)) is-

If "^(n)C_(0)-^(n)C_(1)+^(n)C_(2)-^(n)C_(3)+...+(-1)^(r )*^(n)C_(r )=28 , then n is equal to ……

The value of .^(n)C_(1)+.^(n+1)C_(2)+.^(n+2)C_(3)+"….."+.^(n+m-1)C_(m) is equal to

If .^(n)C_(7)=.^(n)C_(2) , then find .^(n)C_(2) .

If .^(n)C_(3)=.^(n)C_(2) , then find .^(n)C_(2) .

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n)

Find n and r if .^(n)C_(r):^(n)C_(r+1):^(n)C_(r+2)=1:2:3 .

Find the sum of the series .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1).^(n)C_(n)x^(n) and hence show that , .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1)^(n)C_(n)=(n+2)2^(n-1)

The value of ,^nC_0 + ^(n+1)C_1 +^(n+2)C_2+……+^(n+k)C_k is equal to

Find the sum .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "……" + n xx .^(n)C_(n) .