Question

The sum of infnite terms of a G.P. is x and on

squaring each term of it, the sum will be y, then the

common ratio of this series is​

Answer 1

Answer:

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Step-by-step explanation:

Given the sum of infinite terms of a G.P. = x

Let a be the first term and r be the common ratio,

The series is a, ar, ar2…

S = a/(1-r) = x …(i)

a = x(1-r)

When the terms are squared, it becomes a2, a2r2, a2r4 …

Sum = a2/(1-r2) = y …(ii)

Substitute a in above equation

x2(1-r)2/(1-r2) = y

x2(1-r)2/(1+r)(1-r) = y

x2(1-r)/(1+r) = y

x2/y = (1+r)/(1-r)

Applying componendo dividendo rule

(x2-y)/(x2+y) = [(1+r)-(1-r)]/ (1+r)+(1-r)

(x2-y)/(x2+y) = 2r/2

(x2-y)/(x2+y) = r

So r = (x2-y)/(x2+y)