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Evaluate : sum(n = 1)^infty tan^-1(1/(n^...

Evaluate : `sum_(n = 1)^infty tan^-1(1/(n^2 + n + 1))`

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`pi/4`
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PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. Find the interval in which , cos^-1 x gt sin^-1 x.

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  2. Solve the equation sin^-1 6x + sin^-1 6sqrt3 x = -pi/2

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  3. Evaluate : sum(n = 1)^infty tan^-1(1/(n^2 + n + 1))

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  4. If tan^-1 x + tan^-1 2x + tan^-1 3x = pi, then:

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  5. The number of value of 'x' in the interval [0 , 3pi] satisfying the eq...

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  6. The most general solution , satisfying the equation cos theta = 1/sqrt...

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  7. The number of solution of 16^(sin^2 x) + 16^(cos^2 x) = 10 : 0 le x le...

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  8. The equation sin^6 x + cos^6 x = k possesses solution if

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  9. If 3^(sin 2x + 2 cos^2 x) + 3^( 1 - sin 2x + 2 sin^2 x) = 28, then tan...

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  10. If sin^-1 x - cos^-1 x = pi/6 then x is

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

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  12. The value of tan (pi/4 + 1/2 cos^-1(2/3))+tan(pi/4 - 1/2 cos^-1 (2/3))...

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  13. The principal value of sin^-1 (-sqrt3/2)+cos^-1 cos((7pi)/6) is

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  14. The value of tan (pi/4 + 1/2 cos^-1(2/3))+tan(pi/4 - 1/2 cos^-1 (2/3))...

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  15. The value of cos^-1 x + cos^-1 {x/2 + sqrt3/2 cdot sqrt(1 - x^2)}, x g...

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  16. Value of cos^-1 sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))) , x ge 0 is

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  17. The value of tan^2 (sec^-1 2)+ cot^2(cosec^-1 3) is

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  18. 2 cos^-1 x = sin^-1(2xsqrt(1 - x^2)) is valid for

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  19. If 0 le x le 3pi , 0 le y le 3pi and cos x cdot sin y = 1 , then the p...

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  20. The number of solution of the equation x^3 + x^2 + 4x + 2 sin x = 0 , ...

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