Question

Sigma notation

Answer 1

this is an arithmetic series.
you are summing the first 12 terms (from n=1 to n=12)

in arithmetic series, \(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ k } f(n)=\color{red}{\frac{1}{2}\times \left(a_1+a_k\right)}\times \color{blue}{k}}\)

Answer 2

the red is the average term, and k is the number of terms

Answer 3

the k (in blue) is number of terms

Answer 4

or you can use wolfram

Answer 5

you can't get a decimal

Answer 6

impossible

Answer 7

you are adding integers

Answer 8

the sum is not 29.

Answer 9

instead of guessing, lets go ahead and evaluate it

Answer 10

you used it incorrectly

Answer 11

\(\large {
\sum\limits_{n=1}^{12}\ 2n+5 \iff
S_{\color{brown}{ n}}=\cfrac{{\color{brown}{ n}}}{2}(a_1+a_{\color{brown}{ n}})\to \cfrac{{\color{brown}{ 12}}}{2}(7+a_{\color{brown}{ 12}})
}\)

Answer 12

\(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ k } f(n)=\frac{1}{2}\times \left(\color{red}{a_1}+\color{green}{a_k}\right)\times \color{blue}{k}}\)

\(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ 12} (2n+5)=\frac{1}{2}\times \left(\color{red}{a_1}+\color{green}{a_{12}}\right)\times \color{blue}{k}}\)

\(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ 12 } (2n+5)=\frac{1}{2}\times \left(\color{red}{[2(1)+5]}+\color{green}{[2(12)+5]}\right)\times \color{blue}{k}}\)

Answer 13

\(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ 12 } (2n+5)=\frac{1}{2}\times \left(\color{red}{7}+\color{green}{29}\right)\times \color{blue}{12}}\)

Answer 14

( and again, 29 is just the 12th term, so it is clearly not the SUM of the 12 terms. )

Answer 15

do you understand my posts, or are they an abstruse latex dump?

Answer 16

Okay, I'm waiting for the latex to load. Hold on.

Answer 17

oh, it is laggy.... that happens... i b bak

Answer 18

Is the last step 18 x 12?

Answer 19

yes,

Answer 20

or, you could have just canceled 1/2 with the 12, but that doesn't matter

Answer 21

216 is the answer?

Answer 22

yup:)

Answer 23

Thank you