Question

I need help finding the answer to this question on edge.

Answer 1

6

Explanation:

We need to evaluate :-

`\rm\implies \displaystyle\rm\sum^4_n (-1)^n (3n + 2 )`

Here the
`\Sigma` is the sum operator . And here we need to find the sum from n = 1 to n = 4 . We can write it as ,

`\rm\implies (-1)^1 ( 3*1 +2) + (-1)^2 ( 3*2+2) + (-1)^3(3*3+2) + (-1)^4(3*4+2)`

Now we know that for odd powers of -1 , we get -1 and for even powers we get 1 . Therefore ,

`\rm\implies -1 ( 3 + 2 ) + 1 (6+2)+-1(9+2)+1(12+2)`

Now add the terms inside the brackets and then multiply it with the number outside the bracket . We will get ,

`\rm\implies -1 * 5 + 1 * 8 + -1*11 + 1*14 \\\\\rm\implies -5 + 8 - 11 + 14 \\\\\rm\implies\boxed{\quad 6 \quad}`

Hence the required answer is 6.