Home
Class 12
MATHS
The sum of the series (1)/(1xx2).^(25...

The sum of the series
`(1)/(1xx2).^(25)C_(0)+(1)/(2xx3).^(25)C_(1)+(1)/(3xx4).^(25)C_(2)+....+(1)/(26xx27).^(25)C_(25)`

A

`(2^(27)-1)/(26xx27)`

B

`(2^(27)-28)/(26xx27)`

C

`(1)/(2)((2^(26)+1)/(26xx27))`

D

`(2^(26)-1)/(52)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

(1)/(1xx2)""^(25)C_(0)+(1)/(2xx3)""^(25)C_(1)+(1)/(3xx4)""^(25)C_(2)+…+(1)/(26xx27)""^(25)C_(25) is -

The sum of the series 1/(1x2) *(25)C0+1/(2x3) *25C_1+1/(3x4) *25C2+....+1/(26x27)* 25C_25

The sum of the series 1+(1)/(2)""^(n)C_(1)+(1)/(3)""^(n)C_(2)+…+(1)/(n+1)""^(n)C_(n) is equal to-

Find the sum to n terms of each of the series in 1/(1xx2)+1/(2xx3)+1/(3xx4)+.......

Find the sum to n terms of the series 1//(1xx2)+1//(2xx3)+1//(3xx4)+....+1//n(n+1)

Find the value of .^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10) .

The value of 1000[(1)/(1xx2)+(1)/(2xx3)+(1)/(3xx4)+.....+(1)/(999xx1000)] is equal to -

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

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

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2n+1) 2^(n) .