The first term of an infinitely decreasing G.P. is unity and its sum is S. The sum of the squares of the terms of the progression is
A
S2S−1
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B
S22S−1
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C
S2−S
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D
S2
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Solution
The correct option is BS22S−1 Let common ratio is r<1 Then G.P is 1,r,r2,r3,...∞ S=1+r+r2+r3+...∞ ⇒S=11−r Then G.P formed by squaring the terms 1,r2,r4,r6,...∞ S′=11−r2=1(1−r)(1+r)=S22S−1.