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If `a_1,a_2,a3,...,a_n`are in A.P then show that `1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n)`

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If a_(1) ge 0 for all t and a_(1), a_(2), a_(3),….,a_(n) are in A.P. then show that, (1)/(a_(1)a_(3)) + (1)/(a_(3)a_(5)) +...+ (1)/(a_(2n-1).a_(2n+1)) = (n)/(a_(1)a_(2n+1))

If a_1, a_2,...... ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> n

If a_(1), a_(2), a_(3),…, a_(n) be in A.P. Show that, (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) +….+(1)/(a_(n-1)a_(n)) = (n-1)/(a_(1)a_(n))

If a_(1), a_(2), a_(3), …., a_(n) are in H.P., prove that, a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) +…+ a_(n-1)a_(n) = (n-1)a_(1)a_(n)

If a_1,a_2,.....a_n are in H.P., then the expression a_1a_2 + a_2a_3 + ... + a_(n-1)a_n is equal to

If a_(1), a_(2) , a_(3),…,a _(n+1) are in A. P. then the value of (1)/(a _(1)a_(2))+(1)/(a_(2)a_(3))+(1)/(a_(3)a_(4))+...+(1)/(a_(n)a_(n+1)) is-

If a_(1) ge 0 for all t and a_(1), a_(2), a_(3),….,a_(n) are in A.P. then show that, (1)/(sqrt(a_(1))+sqrt(a_(2)))+(1)/(sqrt(a_(2))+sqrt(a_(3)))+ (1)/(sqrt(a_(n-1))+sqrt(a_(n))) = (n-1)/(sqrt(a_(1))+sqrt(a_(n)))

If the sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)

If the coefficients of four consecutive terms in the expansion of (1+x)^n are a_1,a_2,a_3 and a_4 respectively. then prove that a_1/(a_1+a_2)+a_3/(a_3+a_4)=2a_2/(a_2+a_3).

If a_1, a_2,a_3, ,a_n is an A.P. with common difference d , then prove that "tan"[tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+......+tan^(-1)(d/(1+a_(n-1)a_n))]=((n-1)d)/(1+a_1a_n)

UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2016-EXERCISE
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  3. Show that the area of the triangle formed by the lines y = m(1) x + c(...

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  4. Find the value of cos B for the triangle formed by joining the points ...

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  5. Evlauate lim(xrarr0)(cot2x-cosec2x)/x

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  6. Find from the first principle,the derivative of f(x)=e^(x^2)at x=1.

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  7. Prove the following by contradiciton ."The sum of a rational and an ir...

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  8. Check the validity of the following compound propostions :"72 is a mul...

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  9. Check the validity of the following compound propostions :"120 is a mu...

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  10. Two students Anil and Ashima appeared is an examination. The probabili...

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  11. Find the coefficient of variation of the following data:

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  12. Find the general solution of x and y satisfying the equation 5sinx.cos...

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  13. Find the domain of definition and range of the function f(x)=x/(1+x^2)...

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  14. If f(x)=ax^2+bx+cand f(2)=1,f(3)=6,f(-1)=10,then find the value of f(1...

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  15. If z=x+iy and |z-1|+|z+1|=4,then show that 3x^2+4y^2=12,where i=sqrt-1

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  16. In how many ways can 6 boys and 4 girls be seated in a round table so ...

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  17. If a1,a2,a3,...,anare in A.P then show that 1/(a1a2)+1/(a2a3)+1/(a3a4)...

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  18. Solve :(|x|-2)/(|x|-3)ge0,where x in R and x!=+-3

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  19. If the extremitied of a focal chord of the parabola y^2=4axbe (at1^2,2...

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