The first term of an infinitely decreasing GP. is unity and its sum is S. The sum of the squares of the terms of the progression is :

Question

The first term of an infinitely decreasing GP. is unity and its sum is S. The sum of the squares of the terms of the progression is : (A) ( S /2 S -1) (B) ( S 2/2 S -1) (C) ( S /2- S ) (D) S 2

Tardigrade Admin · Accepted Answer

S = a + ar + ar 2+ ........ S=1+r+r2+r3+ ldots ldots . . . . . . . (a=1) S =(1/1- r ) ⇒ 1- r =(1/ S ) ⇒ r =1-(1/ S ) ⇒ ( S -1/ S )= r text Now E = a 2+( ar )2+(a ar 2)2+ ...... E = a 2+ a 2 r 2+ a 2 r 4+ ..... =( a 2/1- r 2)=(1/1-(( S -1) S )2)=( S 2/ S 2- S 2-1+2 S )=( S 2/2 S -1)

Q. The first term of an infinitely decreasing GP. is unity and its sum is S. The sum of the squares of the terms of the progression is :

$\frac{S}{2 S - 1}$

$\frac{S ^{2}}{2 S - 1}$

$\frac{S}{2 - S}$

$S^{2}$

Q. The first term of an infinitely decreasing GP. is unity and its sum is S. The sum of the squares of the terms of the progression is :

2S−1S​

2S−1S2​

2−SS​

S2

S=a+ar+ar2+ ........ S=1+r+r2+r3+…….......(a=1) S=1−r1​⇒1−r=S1​⇒r=1−S1​⇒SS−1​=r Now E=a2+(ar)2+(aar2)2+...... E=a2+a2r2+a2r4+ ..... =1−r2a2​=1−(SS−1​)21​=S2−S2−1+2SS2​=2S−1S2​

$\frac{S}{2 S - 1}$

$\frac{S ^{2}}{2 S - 1}$

$\frac{S}{2 - S}$

$S^{2}$