Question

The sum of the series 1.3² + 2.5² + 3.7² + .... upto 20 terms is ______.

Options

• 188090

• 180890

• 189820

• 180889

Answer 1

The sum of the series 1.3² + 2.5² + 3.7² + .... upto 20 terms is 188090.

Explanation:

1.3² + 2.5² + 3.7² +  ...... up to 20 terms

= `sum_(r = 1)^20n(2n + 1)^2`

= `sum_(r = 1)^20(4n^3 + 4n^2 + n)`

= `4sum_(r = 1)^20n^3 + 4sum_(r = 1)^20n^2 + sum_(r = 1)^20n`

= `4((20 xx 21)/2)^2 + 4((20 xx 21 xx 41)/6) + (20 xx 21)/2`

= (420)² + 11480 + 210

= 188090