badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12

                        

If first terms of a decreasing infinite GP is 1 and sum is S, then sum of squares of its terms is??

9 years ago

Answers : (2)

aatish agrawal
32 Points
							

sum of infinite term in  G.P is a/(1-r). (where a is 1st term, and r is the ratio)

so here in this problem, 1/(1-r)=S    (Since a=1)

solving it u will get; r =1 - 1/s

since terms of a G.P are given by a, ar ,ar^2,ar^3..........and so on

so here u will get the following series...

i.e 1 + (1- 1/s) + (1-1/s)^2 + (1-1/s)^3+..........

on squaring each term u will get,

1^2 + (1- 1/s)^2 + (1 - 1/s)^4 +(1-1/s)^6.........[r =(1-1/s)^2] in this case                                     (1)

so the required sum of this series  is 

s'=1 /(1 -r) substitute value of r from (1)

finally u will get s' =s^2/(2s-1) ans..   .hope my answer will satisfy u.

9 years ago
vikas askiitian expert
509 Points
							

let the GP is a + ar + ar2 + ar3 ...............infinity

sum of infinite GP S = a/1-r      

                         S = 1/1-r                     (a=1)

                        r = S-1/S       ..........1

now gp formed after squaring is a2 + a2r2 + a2r4  ...............infinity

its common ratio is r2

 now sum is S1 = a/1-r2 =1/(1-r)(1+r)

   from eq 1 putting value of r

          S1 = S2/(2S-1)

9 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details