1^st term = 2(1)³ + 3(1)² – 1

2^nd term = 2(2)³ + 3(2)² - 1

And so on

Nth term = 2n³ + 3n² – 1

General term be = 2r³ + 3r² – 1

Summation = 1^st term + 2^nd term + …….. + nth term

= 2(1)³ + 3(1)² – 1 + 2(2)³ + 3(2)² - 1 + …….2n³ + 3n² – 1 …(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 substituting the above values in (2)

Summation =