Question

How do you find the sum given `Sigma (i-1)^2+(i+1)^3` from i=1 to 4?

Answer 1

`sum_ (i=1)^4 (i-1)^2+(i+1)^3 = 238`

Explanation:

Let

`S = sum_ (i=1)^4 (i-1)^2+(i+1)^3`

Expanding we have:

`S = (0^2+2^3) + (1^2+3^3) + (2^2+4^3) + (3^2+5^3)`
`\ \ = 8 + (1+27) + (4+64) + (9+125)`
`\ \ = 8 + 28 + 68 + 134`
`\ \ = 238`