ii. | Sn | = | n2(n+1)2 | ||||||||
4 | |||||||||||
Sol. | Sn | = | n2(n+1)2 | ||||||||
4 | |||||||||||
∴ | S1 | = | 12(1+1)2 | = | 1(2)2 | = | 1×4 | = | 4 | = | 1 |
4 | 4 | 4 | 4 | ||||||||
∴ | S2 | = | 22(2+1)2 | = | 4(3)2 | = | 4×9 | = | 36 | = | 9 |
4 | 4 | 4 | 4 | ||||||||
∴ | S3 | = | 32(3+1)2 | = | 9(4)2 | = | 9×16 | = | 9×4 | = | 36 |
4 | 4 | 4 |
We know that,
t1 = S1 = 1
t2 = S2 – S1 = 9 – 1 = 8
t3 = S3 – S2 = 36 – 9 = 27
∴ The first three terms of the sequence are 1, 8 and 27.
