Let S = 2 + 5 + 10 + 17 + 26 + …………. + n

By shifting each term by one

S = 2 + 5 + 10 + 17 + 26 + …………. + nth ……..(1)

S = 2 + 5 + 10 + 17 + …………. + (n - 1)th + nth ….(2)

by (1) - (2) we get

0 = 2 + 3 + 5 + 7 + 9 + …….nth - (n - 1)th - nth

Nth = 2 + (3 + 5 + 7 + 9 + …….2r + 1) ……….(3)

Nth = 2 + (summation of first (n - 1)th term)

we know,

Substituting the above given value in (3)

nth=n² - 1 + 2

general term=r² - 1 + 2

thus

S = 2 + 5 + 10 + 17 + 26 + …………. + nth =

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

(4)

We know

Thus substituting the above values in(4)