Sum of sequences

1.(a)

{a(n)}:2,5,10,17,26,37,50,...,

a(1) = 2 = 1² + 1
a(2) = 5 = 2² + 1
a(3) = 10 = 3² + 1
a(4) = 17 = 4² + 1
a(5) = 26 = 5² + 1
a(6) = 37 = 6² + 1
a(5) = 26 = 7² + 1
.....
General term, a(n) = n² + 1

(b)
Sum of the first n terms
= a(1) + a(2) + a(3) + ..... + a(n)
= (1² + 1) + (2² + 1) + (3² + 1) + ...... + (n² + 1)
= (1² + 2² + 3² + ...... + n²) + n
= [n(n + 1)(2n + 1)/6] + n

2011-07-28 21:57:57 補充：
The answer of (b) may be further simplified as :

Sum of the first n terms
= [n(n + 1)(2n + 1)/6] + n ...... (answer)
= n[(n + 1)(2n + 1) + 6]/6
= n(2n² + 3n + 7)/6 ...... (simplified answer)