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If 1+(1/2^2)+(1/3^2)+(1/4^2)+(1/5^2)+...= x then the value of 1+(1/2^2)+(1/4^2)+(1/6^2)+(1/8^2)+... is?


Let's write out the terms so it's a little more readable.
1 + 1/4 + 1/9 + 1/16 + 1/25 + ... = x
and
1 + 1/4 + 1/16 + 1/36 + 1/64 +... = ?
Can you see that the second series is
1 + 1/4(1 + 1/4 + 1/9 + 1/16 + ...)=1+1/4x ?

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Gina

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