Our class was given a "ridiculously hard" extension maths project. I've been able to answer all the questions except one. This is the problem:

 

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The variable [math]x[/math] is defined: [math]x = 1/2^2 + 1/3^2 + 1/4^2 + 1/5^2 ...[/math]

 

Express the infinite sum [math]1 + 1/2^2 + 1/4^2 + 1/6^2 + 1/8^2 ...[/math] in terms of [math]x[/math].

 

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Could someone please give me a clue to solving this? I don't even know where to start. The teacher who wrote the project has received quite a lot of complaints lol.

Compare the two series on a term-by-term basis. It might help to temporarily discard some of the leading terms of the target series. You can always add those discarded terms back in later.

Ah... I get it now