What is the value of E(-1) n (3n+2)?

Question

asked Dec 23, 2022 55.5k views

1 Answer

Luong Truong · Answer 1 · 2022-12-27T21:41:43+0000

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Step-by-step explanation:

The weird looking E symbol is the greek uppercase letter sigma. It refers to a sum.

It tells us to add up terms in the form (-1)^n*(3n+2) where n is an integer ranging from n = 1 to n = 4.

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If n = 1, then we have

(-1)^n*(3n+2) = (-1)^1*(3*1+2) = -5

Let A = -5 as we'll use it later.

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If n = 2, then

(-1)^n*(3n+2) = (-1)^2*(3*2+2) = 8

Let B = 8 since we'll use this later as well

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If n = 3, then

(-1)^n*(3n+2) = (-1)^3*(3*3+2) = -11

Let C = -11

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If n = 4, then

(-1)^n*(3n+2) = (-1)^4*(3*4+2) = 14

Let D = 14.

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We'll add up the values of A,B,C,D to get the final answer

A+B+C+D = -5+8+(-11)+14 = 6

This means that

$\displaystyle \sum_(n=1)^(4)(-1)^n(3n+2) = 6$