Given: 2 × 4 + 4 × 6 + 6 × 8 + ……………..

The nth term would be from given series 2n × (2n + 2)

The general term would be from given series 2r × (2r + 2)

Thus 20^th term be 2(20) {2(20) + 2} = 40 × 42 = 1680

Summation=1^st term + 2^nd term + …… + 20th term

= 2 × 4 + 4 × 6 + 6 × 8 + …… 40 × 42 (1)

We know

Thus

From (1) we have

Summation =

We know by property that:

∑axⁿ + bx^{n - 1} + cx^{n - 2}…….d₀=a∑xⁿ + b∑x^{n - 1} + c∑x^{n - 2}…….. + d₀∑1

Thus,

(2)

We know

Thus

Thus substituting in above equation in (2)

=4(10)(7)(41) + 4(10)(21)

=12320