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If alpha1 , alpha2, ......, alphan are i...

If `alpha_1 , alpha_2, ......, alpha_n` are in A.P, whose common difference is d , show that
`sin d [ sec alpha_1 sec alpha_2 + sec alpha_2 sec alpha_3 +.......+ sec alpha_(n - 1) sec alpha_n] = tan alpha_n - tan alpha_1`

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
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  3. If alpha1 , alpha2, ......, alphan are in A.P, whose common difference...

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  6. If a1. a2 ....... an are positive and (n - 1) s = a1 + a2 +.....+an th...

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  7. Find the sum to n terms of the series 1/(1 + 1^2 + 1^4) + 2/(1 + 2^2...

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  8. Evaluate , S =sum(n = 0)^infty 2^n/(a^(2^n) + 1) (where a gt 1)

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  9. Evaluate, sum(i = 0)^iinfty sum(j = 0)^infty sum(k = 0)^infty 1/(3^i c...

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  10. If a, b, c, d are four distinct numbers in A.P. , show that 1/a + 1/d ...

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  11. Let An = (3/4) -(3/4)^2 + (3/4)^3 +.....+(-1)^(n - 1) (3/4)^n , Bn = 1...

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  12. Let the harmonic mean of two positive real numbers a and b be 4. If q ...

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  13. Suppose that all the terms of an arithmetic progression (A.P) are natu...

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  14. The sum of first 9 terms of the series 1^3/1 + (1^3 + 2^3)/(1 + 3) + (...

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  16. If sin^-1 ( x-x^2/2 + x^3/4 - x^4/8 +....) = pi/6 where absx lt 2 then...

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  17. Let d(n) denotes the number of divisors of n including 1 and itself. T...

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