Question -
Answer -
Let Tn bethe nth term and Sn be the sum to n terms of the givenseries.
We have,
Sn = 2+ 5 + 10 + 17 + 26 + …………. + Tn-1 + Tn … (1)
Equation (1) can berewritten as:
Sn = 2+ 5 + 10 + 17 + 26 + …………. + Tn-1 + Tn ……..(2)
By subtracting (2)from (1) we get
Sn = 2+ 5 + 10 + 17 + 26 + …………. + Tn-1 + Tn
Sn = 2+ 5 + 10 + 17 + 26 + …………. + Tn-1 + Tn
0 = 2 + [3 + 5 + 7 + 9+ … + (Tn – Tn-1)] – Tn
The difference betweenthe successive terms are 3, 5, 7, 9
So these differencesare in A.P
Now,
∴ The sum of the seriesis n/6 (2n2 + 3n + 7)