Home
Class 11
MATHS
Let S e the sum, P the product, adn R th...

Let `S` e the sum, `P` the product, adn `R` the sum of reciprocals of `n` terms in a G.P. Prove that `P^2R^n=S^ndot`

Text Solution

Verified by Experts

Let G.P. be
`a,ar,ar^2,....ar^(n−1)`
`S=(a(r^n−1))/(r-1)​`
`P=a^nr^(((n−1)n)/2​)`
`R=1/a​+1/(a^r)​+1/(ar^2)`
​`=(1​(r^0+r^(−1)+r^(−2)+....))/a`
`=1/a​×r^0(r^n−1)/(r^n−1​)`
`=1/a​(1−r^n×r​)/(r^n(1−r))`
`=((1−r^n)(r^(1−n))​)/(a(1−r))`
...
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|24 Videos

  • SEQUENCES AND SERIES

    NCERT ENGLISH|Exercise EXERCISE 9.2|18 Videos

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 2.3|5 Videos

  • SETS

    NCERT ENGLISH|Exercise EXERCISE 1.5|7 Videos

Similar Questions

Explore conceptually related problems

Let S be the sum, P the product, and R the sum of reciprocals of n terms in a G.P. Prove that P^2R^n=S^ndot

if S is the sum , P the product and R the sum of reciprocals of n terms in G.P. prove that P^2 R^n=S^n

if S is the sum , P the product and R the sum of reciprocals of n terms in G.P. prove that P^2 R^n=S^n

If S is the sum, P the product and R the sum of the reciprocals of n terms in G.P., prove that P^(2)= ((S)/(R))^(n) .

Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. then P^2R^3: S^3 is equal to (a) 1:1 (b) (common ratio)^n :1 (c) (First term)^2(common ratio)^2 (d) None of these

If S be the sum, p the product and R the sum of the reciprocals of n terms of a G.P., then (S/R)^n is equal to

If S be the sum P the product and R be the sum of the reciprocals of n terms of a GP then p^2 is equal to S//R b. R//S c. (R//S)^n d. (S//R)^n

If S_n denotes the sum of first n terms of an A.P., prove that S_(12)=3(S_8-S_4) .

If S_n denotes the sum of the first n terms of an A.P., prove that S_(30)=3(S_(20)-S_(10)) .

If S_1 be the sum of (2n+1) term of an A.P. and S_2 be the sum of its odd terms then prove that S_1: S_2=(2n+1):(n+1)dot