Question

If S₁ , S₂ , S₃ , ........ , S_2n are the sums of infinite geometric series whose first terms are respectively 1 , 2 , 3 , ........ , 2 n and common ratio are respectively , 1/2 , 1/3 , ........ , 1/(2n -1) , find the value of , S₁² + S₂² + ........ + S²_{2n - 1} .

Answer 1

⇒ (2n(2n + 1)(2 x 2n + 1))/6 - 1