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Evaluate the sum of the first n terms of the series 1/(1+1^2+1^4) + 2/(1+2^2+2^4) + 3/(1+3^2+3^4) + ...

1. (n^2+n-1)/(2(n^2+n+1))
2. (n^2+n)/(2(n^2+n+1))
3. (n^2-n+1)/(n^2+n+1)
4. (n^2-n)/(2(n^2+n+1))

Correct answer: (n^2-n+1)/(n^2+n+1)

Solution

The correct option simplifies the series by recognizing the pattern in the denominators and numerators, leading to a formula that accurately represents the sum of the first n terms in a consistent manner.

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