Pillow-Problems: Problem #32

Problem #31 | Problem #38
For more information on this collection, see Pillow-Problems by Charles L. Dodgson (Lewis Carroll).

Problem:

Sun the Series 1 · 5 + 2 · 6 + &c. (1) to n terms; (2) to 100 terms.

Answer:

(1)

n · (n + 1) · (2n + 13)

6

;

(2) 358550.

Solution:

The nth term is n · (n + 4);

∴ the (n + 1)th term is (n + 1) · (n + 5) = (n + 1) · {(n + 2) + 3},