Question

calculus ..... I know how to do all 3 of theM EXCEPT THE FIRST ONE.. screen shot attached

Answer 1

\[\sum \limits_{i=1}^n \dfrac{8i+7}{n^2}\]

you can pull out n^2 because it got nothing to do with the index variable "i"

Answer 2

i have a previous one that i did

Answer 3

\[\sum \limits_{i=1}^n \dfrac{8i+7}{n^2} = \frac{1}{n^2} \sum \limits_{i=1}^n (8i+7)\]

Answer 4

I don't get what it's asking though?

Answer 5

its just asking u work that sum and express it in terms of n

Answer 6

thats should be the same exact answer as the one i had then? did you see the example that i got wrong?

Answer 7

you should get answer in terms of "n"

Answer 8

because the sum form i=1 to n depends on "n" right ?

Answer 9

yes it does

Answer 10

\[\begin{align}

\sum \limits_{i=1}^n \dfrac{8i+7}{n^2} &= \frac{1}{n^2} \sum \limits_{i=1}^n (8i+7)\\~\\
&= \frac{1}{n^2}\left[ \sum \limits_{i=1}^n 8i+ \sum \limits_{i=1}^n7\right]\\~\\

&= \frac{1}{n^2}\left[ 8\sum \limits_{i=1}^n i+ \sum \limits_{i=1}^n7\right]\\~\\

\end{align}\]

Answer 11

whats the sum of first "n" natural numbers ?

Answer 12

what do you get when u add 7 for n times ?

Answer 13

\[\begin{align}

\sum \limits_{i=1}^n \dfrac{8i+7}{n^2} &= \frac{1}{n^2} \sum \limits_{i=1}^n (8i+7)\\~\\
&= \frac{1}{n^2}\left[ \sum \limits_{i=1}^n 8i+ \sum \limits_{i=1}^n7\right]\\~\\

&= \frac{1}{n^2}\left[ 8\sum \limits_{i=1}^n i+ \sum \limits_{i=1}^n7\right]\\~\\

&= \frac{1}{n^2}\left[ 8\frac{n(n+1)}{2}+ 7n\right]\\~\\

\end{align}\]

Answer 14

simplify

Answer 15

I tried writing that as well, but it's just numbers no "N" expression in the answer

Answer 16

do u get what i'm saying?

Answer 17

the system doesn't want any "n" in the asnwer

Answer 18

S(n) depends on "n" here, so i don't know how u gona fool the system

Answer 19

http://www.wolframalpha.com/input/?i=%5Csum+%5Climits_%7Bi%3D1%7D%5En+%5Cdfrac%7B8i%2B7%7D%7Bn%5E2%7D

Answer 20

How do u know how to put it in wolfram
i tried using it once, and it gave me wrong answers, or i don't know how to use it in other words

Answer 21

wolfram understands latex

Answer 22

below also works :
http://www.wolframalpha.com/input/?i=sum+%288i%2B7%29%2F%28n%5E2%29%2C+i%3D1+to+n