Answer :

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 + bxn - 1 + cxn - 2…….d0=a∑xn + b∑xn - 1 + c∑xn - 2…….. + d0∑1


(4)


We know




Thus substituting the above values in(4)




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