Question -
Answer -
Let Tn bethe nth term and Sn be the sum to n terms of the givenseries.
We have,
Sn = 1+ 3 + 6 + 10 + 15 + …………. + Tn-1 + Tn … (1)
Equation (1) can berewritten as:
Sn = 1+ 3 + 6 + 10 + 15 + …………. + Tn-1 + Tn ……..(2)
By subtracting (2)from (1) we get
Sn = 1+ 3 + 6 + 10 + 15 + …………. + Tn-1 + Tn
Sn = 1+ 3 + 6 + 10 + 15 + …………. + Tn-1 + Tn
0 = 1 + [2 + 3 + 4 + 5+ … + (Tn – Tn-1)] – Tn
The difference betweenthe successive terms are 2, 3, 4, 5
So these differencesare in A.P
Now,
∴ The sum of the seriesis n/6 (n+1) (n+2)