Home
Class 12
MATHS
sum(r=1)^(n) tan^(-1)(2^(r-1)/(1+2^(2r-1...

`sum_(r=1)^(n) tan^(-1)(2^(r-1)/(1+2^(2r-1)))` is equal to a)`tan^(-1)(2^n)` b)`tan^(-1)(2)^n-pi/4` c)`tan^(-1)(2^(n+1))` d)`tan^(-1)(2^(n+1))-pi/4`

A

`tan^(-1)(2^n)`

B

`tan^(-1)(2)^n-pi/4`

C

`tan^(-1)(2^(n+1))`

D

`tan^(-1)(2^(n+1))-pi/4`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

2"tan"^(-1)(1/(3))+"tan"^(-1)(1/(4)) is equal to

tan ( 2 tan^(-1) ((2)/(5))) is equal to

Prove that tan^(-1)(2/11) + tan^(-1)(7/24) = tan^(-1)(1/2)

tan^(-1)""(m)/(n)-tan^(-1)""(m-n)/(m+n) is equal to a) tan^(-1)""(n)/(m) b) tan^(-1)""(m+n)/(m-n) c) (pi)/(4) d) tan^(-1)((1)/(2))

The value of tan^(-1)((sqrt(3))/(2))+tan^(-1)((1)/(sqrt(3))) is equal to a) tan^(-1)((5)/(sqrt(3))) b) tan^(-1)((2)/(sqrt(3))) c) tan^(-1)((1)/(2)) d) tan^(-1)((1)/(3sqrt(3)))

tan [ 3 tan^(-1) ((1)/(5)) - (pi)/(4) ] is equal to

Prove that 2 tan^(-1)(1/2) + tan^(-1)(1/7) = tan^(-1)(31/17)

int (dx)/((x + 1) sqrt(x)) is equal to a) tan^(-1) sqrt(x) + C b) 2 tan^(-1) x + C c) 2 tan^(-1) (sqrt(x)) + C d) tan^(-1) (x^((3)/(2))) + C

Prove that tan ^(-1) (1/7)+tan ^(-1)( (1)/(13))=tan ^(-1)( 2/9)

If a_(1), a_(2), a_(3), ………., a_(n) are in AP with common difference 5 and if a_(i)a_(j) ne -1 for i, j = 1, 2, …….., n, then tan^(-1)((5)/(1+a_(1)a_(2))) + tan^(-1)((5)/(1+a_(2)a_(3))) +……..+ tan^(-1)((5)/(1+a_(n-1)a_(n))) is equal to a) tan^(-1)((5)/(1+a(n)a_(n-1))) b) tan^(-1)((5)/(1+a(n)a_(n))) c) tan^(-1)((5n-5)/(1+a(n)a_(n+1))) d) tan^(-1)((5n-5)/(1+a_(1)a_(n)))