Write the sum of the series 2+4+6+8+...+2n.

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Solution

$L e t T_{n} be the given series and S_nbe the sum of the given series. ∴ T_{n} = 2 n ∴ S_{n} = \sum_{k - 1}^{n} T_{k} = \sum_{k - 1}^{n} 2 k = 2 \sum_{k - 1}^{n} k = 2 [\frac{n (n + 1)}{2}] = n (n + 1) H e n c e, S_{n} = n (n + 1)$

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