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If `a_1,a_2,a_3, ,a_n` are in A.P., where `a_i >0` for all `i` , 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))dot`

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If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_1)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_1)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

If a_r>0, r in N and a_1.a_2,....a_(2n) are in A.P then (a_1+a_2)/(sqrta_1+sqrta_2)+(a_2+a_(2n-1))/(sqrta_2+sqrta_3)+.....+(a_n+a_(n+1))/(sqrt a_n+sqrta_(n+1))=

If a_1,a_2,a_3, ,a_n are an A.P. of non-zero terms, prove that 1/(a_1a_2)+1/(a_2a_3)++1/(a_(n-1)a_n)= (n-1)/(a_1a_n)

If a_1,a_2,a_3,…………..a_n are in A.P. whose common difference is d, show tht sum_2^ntan^-1 d/(1+a_(n-1)a_n)= tan^-1 ((a_n-a_1)/(1+a_na_1))

If A,A_1,A_2 and A_3 are the areas of the inscribed and escribed circles of a triangle, prove that 1/sqrtA=1/sqrt(A_1)+1/sqrt(A_2)+1/sqrt(A_3)

If a_1, a_2, a_3, ,a_(2n+1) are in A.P., then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_(2n)-a_2)/(a_(2n)+a_2)++(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to a. (n(n+1))/2xx(a_2-a_1)/(a_(n+1)) b. (n(n+1))/2 c. (n+1)(a_2-a_1) d. none of these

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

Let a_1, a_2, a_3, ...a_(n) be an AP. then: 1 / (a_1 a_n) + 1 / (a_2 a_(n-1)) + 1 /(a_3a_(n-2))+......+ 1 /(a_(n) a_1) =

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. the sum of terms equidistant from the beginning and end in an A...

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  2. If a1,a2,a3, ,an are an A.P. of non-zero terms, prove that 1/(a1a2)+...

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  3. If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/...

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  4. The p^(t h) term of an A.P. is a and q^(t h) term is b Prove that t...

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  5. If S1,S2, S3, Sm are the sums of n terms of m A.P. ' s whose first ter...

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  6. Let Sn be the sum of first n terms of an A.P. with non-zero common d...

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  7. If there are (2n+1) terms in A.P., then prove that the ratio of the su...

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  8. The ratio of the sum of n terms of two A.P. s is (7n+1):(4n+27) . Fin...

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  9. Show that x^2+x y+y^2,z^2+xz+x^2, y^2+y z+z^2, are consecutive terms o...

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  10. If a ,b ,c are in A.P., prove that: i.(a-c)^2=4(a-b)(b-c) ii.a^2+c^2...

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  11. Find the sum of all those integers between 100 and 800 each of which o...

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  12. If the sum of m terms of an A.P. is equal to the sum of either the nex...

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  13. Suppose x and y are two real numbers such that the rth mean between xa...

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  14. The sum of two numbers is (13)/6dot An even number of arithmetic means...

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  15. The digits of a positive integer, having three digits, are in A.P. and...

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  16. If x ,y ,z are in A.P. and A1 is the A.M. of xa n dya n dA2 is the A.M...

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  17. A man repays a loan of R s .3250 by paying R s .20 in the first month ...

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  18. If (b+c-a)/a ,(b+c-a)/b ,(b+c-a)/c , are in A.P., prove that 1/a ,1/b ...

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  19. If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a...

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  20. If a ,b ,c are in A.P., prove that 1/(b c),1/(c a),1/(a b), is al...

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