Home
Class 11
MATHS
If a(1), a(2), a(3),……,a(n) are in AP, w...

If `a_(1), a_(2), a_(3),……,a_(n)` are in AP, where `a_(i) gt 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)))`

Text Solution

Verified by Experts

The correct Answer is:
`((n-1)d)/(d(sqrt(a_(n))+ sqrt(a_(1))))`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems -Long Answer Type Question|4 Videos

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems -Objective Type Questions|10 Videos

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Testbook Illustrations for Practice Work|25 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Question of Module)|16 Videos

  • SETS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|28 Videos

Similar Questions

Explore conceptually related problems

If a_(1),a_(2),a_(3),"….",a_(n) are in AP, where a_(i)gt0 for all I, the value of (1)/(sqrta_(1)+sqrta_(2))+(1)/(sqrta_(2)+sqrta_(3))+"....."+(1)/(sqrta_(n-1)+sqrta_(n)) is

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 the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

If a_(1),a_(2),a_(3),"........",a_(n) are in AP with a_(1)=0 , prove that (a_(3))/(a_(2))+(a_(4))/(a_(3))+"......"+(a_(n))/(a_(n-1))-a_(2)((1)/(a_(2))+(1)/(a_(3))"+........"+(1)/(a_(n-2)))=(a_(n-1))/(a_(2))+(a_(2))/(a_(n-1)) .

If a_(1), a_(2), a_(3).,,,,,,,,a_(n) are in A.P and their common difference is d. The value of the series sin d_(1) [sec a_(1).sec a_(2) + sec a_(2).sec a_(3)+ ….+ sec a_(n-1).sec a_(n)] is……..

If a_(i) gt 0 AA I in N such that prod_(i=1)^(n) a_(i) = 1 , then prove that (a + a_(1)) (1 + a_(2)) (1 + a_(3)) .... (1 + a_(n)) ge 2^(n)

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than 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_(3),a_(4) and a_(5) are in AP with common difference ne 0, find the value of sum_(i=1)^(5)a_(i) " when " a_(3)=2 .

If a_(1),a_(2),a_(3),...,a_(n) is an arithmetic progression with common difference d, then evaluate the following expression. tan[tan^(-1)(d/(1+a_(1)a_(2)))+tan^(-1)(d/(1+a_(2)a_(3)))+...+tan^(-1)(d/(1+a_(n-1)*a_(n)))]

Suppose a_(1), a_(2), a_(3),…., a_(49) are in A.P and underset(k=0)overset(12)Sigma a_(4k+1)= 416 and a_(9) + a_(43)= 66 . If a_(1)^(2) + a_(2)^(2)+ ….+ a_(17)^(2)= 140m then m= ……..