1 + X^2 +X^4 + X^6 + X^8 +...= (1-X^2)^-1
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it's a summation starting at 0 and going on to infinity:
x^2n
using this and plugging in values for n, starting at zero, you get the series from your question.
x^2(0) + x^2(1) + x^2(2) + x^2(3) + x^2(4)...
1 + x^2 + x^4 + x^6 + x^8
not sure if this is what you were asking, however.
x^2n
using this and plugging in values for n, starting at zero, you get the series from your question.
x^2(0) + x^2(1) + x^2(2) + x^2(3) + x^2(4)...
1 + x^2 + x^4 + x^6 + x^8
not sure if this is what you were asking, however.
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Uncompleted homework