If S denotes the sum of an infinite G P , S1 denotes the sum of the squares of - Maths - Sequences and Series

Question

If S denotes the sum of an infinite G P , S1 denotes
the sum of the squares of its terms,then prove that the first term
and common ratio are respectively 2SS1/ S2 +
S1 and S2 - S1/ S2 +
S1

Sunanta Meitei · Accepted Answer

Hi!
Here is the solution to your question
Let a be the first term and r the common ratio
of the infinite G P
Then,
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Best wishes!

If S denotes the sum of an infinite G.P. , S1 denotes the sum of the squares of its terms,then prove that the first term and common ratio are respectively 2SS1/ S2 + S1 and S2 - S1/ S2 + S1.

If S denotes the sum of an infinite G.P. , S₁denotes the sum of the squares of its terms,then prove that the first term and common ratio are respectively 2SS₁/ S² + S₁and S²- S₁/ S²+ S₁.