Question

Which expressions are equal to 50Σn(n+6)?

Answer 1

S(n)=(25/3)n(n+1)(2n+19)

Explanation:

sum_(n=1)^k n (6 + n) = 1/6 k (k + 1) (2 k + 19)

`sum_(n=1)^k n (6 + n) = (1/6) k (k + 1) (2 k + 19)\\50(1/6) k (k + 1) (2 k + 19)\\=(25/3)k (k + 1) (2 k + 19)`

This is the equation in general:

substitute n for sum from 1 to n

For sum from k to n, substitute:

S(n)-S(k-1)

Answer 2

Part 1: B and D

Part 2: C

Part 3: 50575

Explanation: