Question

The sum of n terms of the series 2² + 4² + 6² + ........ is ______.

Options

• `("n"("n" + 1)(2"n" + 1))/3`

• `(2"n"("n" + 1)(2"n" + 1))/3`

• `("n"("n" + 1)(2"n" + 1))/6`

• `("n"("n" + 1)(2"n" + 1))/9`

Answer 1

The sum of n terms of the series 2² + 4² + 6² +........ is `underlinebb((2n(n + 1)(2n + 1))/3`.

Explanation:

2² + 4² + 6² + ...... + (2n²)

`\implies 4sum"n"^2` = 2² (1² + 2² + 3² + ..... + n²)

 = `(4"n"("n" + 1)(2"n" + 1))/6`

= `(2"n"("n" + 1)(2"n" + 1))/3`