Home
Class 12
MATHS
Let S(n),n=1,2,3,"…" be the sum of infin...

Let `S_(n),n=1,2,3,"…"` be the sum of infinite geometric series, whose first term is n and the common ratio is `(1)/(n+1)`. Evaluate `lim_(n to oo)(S_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)+"..."+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+"......"+S_(n)^(2))`.

A

`(1)/(2)`

B

`(3)/(4)`

C

1

D

`- (1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - I) Subjective|10 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos

  • SETS

    AAKASH INSTITUTE|Exercise SECTION-I(Aakash Challengers Questions)|5 Videos

Similar Questions

Explore conceptually related problems

Let S_(n),n=1,2,2.... be the sum of infinite geometric series whose first term is n and the common ratio is.(1)/(n+1) .Evaluate lim_(n rarr oo)(S_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)+....+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+...+S_(n)^(2))

If S_(1), S_(2), S_(3),….., S_(n) are the sum of infinite geometric series whose first terms are 1,3,5…., (2n-1) and whose common rations are 2/3, 2/5,…., (2)/(2n +1) respectively, then {(1)/(S_(1) S_(2)S_(3))+ (1)/(S_(2) S_(3) S_(4))+ (1)/(S_(3) S_(4)S_(5))+ ........."upon infinite terms"}=

if S_(n) denotes the sum of n terms of a G.P whose first term is a and common ratio is r then find the sum of S_(1),S_(3),S_(5).........,S_(2)n-1

If S_(1), S_(2), S_(3),...,S_(n) are the sums of infinite geometric series, whose first terms are 1, 2, 3,.., n and whose common rations are (1)/(2), (1)/(3), (1)/(4),..., (1)/(n+1) respectively, then find the values of S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ...+ S_(2n-1)^(2) .

S_(n+3)-3S_(n+2)+3S_(n+1)-S_(n)=0

If S_(1), S_(2),cdots S_(n) , ., are the sums of infinite geometric series whose first terms are 1, 2, 3,…… ,n and common ratios are (1)/(2) ,(1)/(3),(1)/(4),cdots,(1)/(n+1) then S_(1)+S_(2)+S_(3)+cdots+S_(n) =

If S_(1),S_(2),S_(3),"…….",S_(2n) are the same of infinite geometric series whose first terms are respectively 1 , 2, 3,"…….", 2n and common ratio are respectively. 1/2, 1/3, '…..". (1)/(2n+1) .Find the value of S_(1)^(2) + S_(2)^(2) + "……" + S_(2n-1)^(2) .