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If a1,a2,a3,...,aaare in A.P then show t...

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

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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)

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) 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_(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).

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 13-EXERCISE
  1. The coefficient of three consecutive terms in the expansion of (1+x)^n...

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  2. Show that the straight line (a + 2b) x + (a -3b)y + b -a = 0 always p...

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  3. Find the equations of straight line which are perpendicular to the str...

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  4. y = 2x is a chord of the circle x^2 + y^2 -10 x = 0. Find the equation...

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  5. Find the ratio in which the plane 2x + 2y - 2z = 1 divides the line se...

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  6. Evaluate :lim(xrarroo)[(1^(1//x)+2^(1//x)+3^(1//x))/3]

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  7. Differentiate x^(-2/3) with respect to x, with behalf of definition.

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  8. Prove that sqrt3is irrational, (use the method of contradiction)

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  9. If x and y are odd integers, then xy is also an odd integer r examine ...

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  10. The probability of occurrence of at least one event of two events X an...

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  11. If the co-efficient of variation of two frequeny distribution are 58% ...

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  12. Prove that (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

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  13. In /\ABC,Prove that a cos A + b cos B + c cos C = 2a sin B sin C

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

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  15. Solve x^2 -(7 -i)x + (18 -i) = 0 and hence prove that the roots are no...

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  16. The Indian cricket eleven is to be selected out of 15 players. 6 of th...

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  17. Draw the graph and' find the common region of the system of following ...

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  18. If the pointP(at^2,2at) is a end point of a chord of the parabolay^2=...

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  19. In a hyperbola, (a) centre is origin (b) transverse axis along-with x ...

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  20. find the equation of the ellipse whose eccentricities is 1/2, focus i...

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