Write the sum of first n even natural numbers. - Vidyadip

Question

Write the sum of first n even natural numbers.

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Answer

We have, 2 + 4 + 6 + ... up to n terms $\therefore\text{S}_\text{n}=\frac{\text{n}}{2}[2\times2+(\text{n}-1)\times2]$ $=\frac{\text{n}}{2}[4+2\text{n}-2]$ $=\frac{\text{n}}{2}[2\text{n}+2]$ $=\frac{\text{n}}{2}\times2(\text{n}+1)$ $\text{n}(\text{n}+1)$ $\therefore2+4+6+\ ...$ up to n terms = n (n + 1) Hence, the sum of first n even natural numbers is n (n + 1)

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