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sum(r=1)^ntan^-1((xr-x(r-1))/(1+x(r-1)xr...

`sum_(r=1)^ntan^-1((x_r-x_(r-1))/(1+x_(r-1)x_r))=sum_(r=1)^n(tan^-1x_r-tan^-1x_(r-1))=tan^-1x_n-tan^-1x_0, AAn in N`
Answer the following question on above passage:
The sum to infinite terms of the series `cot^-1(2^2+1/2)+cot^-1(2^3+1/2^2)+cot^-1(2^4+1/2^3)+`..... is

A

`pi/4`

B

`pi/2`

C

`pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
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PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. f(x)=sin{cot^-1(x+1)}-cos(tan^-1x) a=costan^-1sincot^-1x b=cos(2cos^-1...

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  2. f(x)=sin{cot^-1(x+1)}-cos(tan^-1x) a=costan^-1sincot^-1x b=cos(2cos^-1...

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  3. sum(r=1)^ntan^-1((xr-x(r-1))/(1+x(r-1)xr))=sum(r=1)^n(tan^-1xr-tan^-1x...

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  4. sum(r=1)^ntan^-1((xr-x(r-1))/(1+x(r-1)xr))=sum(r=1)^n(tan^-1xr-tan^-1x...

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  5. Arrange the followig radicals in increasing order of -I effect. 1,Br,C...

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  6. Match Column-I with Column-II

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  7. The number of values of theta in the interval (-pi/2, pi/2) such that ...

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  8. If a, b, c, d in (0, pi) and b+c ne pi/2 such that 2cosa+6cosb+7cosc+9...

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  9. The value of 1/2{sec^2(tan^-1 2)+cosec^2(cot^-1 3)+tan^2(pi/3)} is equ...

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  10. If x gt 0, then the value of sin{tan^-1((1-x^2)/(2x))+cos^-1((1-x^2)/(...

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  11. If cos^-1(x/2)+sin^-1(x/4)=pi/6, then the value of x is

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  12. Solve: cos^4(x/5)+sin^2(x/5)=1

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  13. Solve: abscot(2x-pi/2)=1/(cos^2 2x)-1

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  14. Solve: 2cos^2x+5cosx+2 ge 0

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  15. Find the points of intersection of the curves y=cosx and y=sin3x if -p...

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  16. Solve for x and y : 2^(1/cos^2x)sqrt(y^2-y+1//2) le 1

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  17. Find the value of tan^-1(1/2tan2A)+tan^-1(cotA)+tan^-1(cot^3A), for 0 ...

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  18. Solve: sin^-1x+sin^-1(1-x)=cos^-1x

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  19. Prove that: tan^-1((c1x-y)/(c1y+x))+tan^-1((c2-c1)/(1+c2c1))+tan^-1((c...

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  20. The value of 'a' for which ax^2 + sin^-1 (x^2 - 2x + 2) + cos^-1 (x^2 ...

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