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

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Answer 1 · 2017-12-16T13:57:43

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

Let

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

Expanding we have:

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

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