Question -
Answer -
Let┬аTn┬аbethe┬аnth term and Sn┬аbe the sum to n terms of the given series.
We have,
Sn┬а= 1+ 3 + 7 + 13 + 21 + тАжтАжтАжтАж. + Tn-1┬а+ Tn┬атАж (1)
Equation (1) can berewritten as:
Sn┬а= 1+ 3 + 7 + 13 + 21 + тАжтАжтАжтАж. + Tn-1┬а+ Tn┬атАжтАж..(2)
By subtracting (2)from (1) we get
Sn┬а= 1+ 3 + 7 + 13 + 21 + тАжтАжтАжтАж. + Tn-1┬а+ Tn
Sn┬а= 1+ 3 + 7 + 13 + 21 + тАжтАжтАжтАж. + Tn-1┬а+ Tn
0 = 1 + [2 + 4 + 6 + 8+ тАж + (Tn┬атАУ Tn-1)] тАУ Tn
The difference betweenthe successive terms are 2, 4, 6, 8
So these differencesare in A.P
Now,
тИ┤ The sum of the seriesis n/3 (n2┬а+ 2)