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Aiswarya Ram Gupta Grade: 12
        

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

6 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.

6 years ago
vikas askiitian expert
510 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)

6 years ago
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