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Evaluate the series 3/1² + 5/(1²+2²) + 7/(1²+2²+3²) +... taken for 11 terms:

1. 7/2
2. 11/4
3. 11/2
4. 60/11

Correct answer: 11/2

Solution

The kth term is (2k+1)/(sum of squares to k) = 6/(k(k+1)) = 6(1/k - 1/(k+1)). Summing 11 terms gives 6(1 - 1/12) = 6*11/12 = 11/2.

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