Summation Notation Practice

1. $\large\displaystyle\sum\limits_{k=1}^{2 }{{(3-k)}}=$

2. $\large\displaystyle\sum\limits_{n=0}^{2 }{{(-n)}}=$

3. $\large\displaystyle\sum\limits_{x=1}^{2 }{{(6x)}}=$

4. $\large\displaystyle\sum\limits_{n=0}^{2 }{{(n)}}=$
   

Source: Khan Academy, https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:geo-series-notation/e/evaluating-basic-sigma-notation
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

1. What is the question asking for?

   $\sum$ tells us to find the sum.

   The question is asking for the sum of the values of ‍$3-k$ from ‍$k = 1$ to ‍$k = 2$.
   

   Evaluating

   ‍$\begin{aligned} \large\displaystyle\sum\limits_{k=1}^{2 }{({3-k})}&= (3-1) + (3-2) \\\\&= 2 + 1 \\\\&= 3\end{aligned}$

   The answer
   

   ‍$\large\displaystyle\sum\limits_{k=1}^{2 }{({3-k})}=3$

   ---

2. What is the question asking for?

   $\sum$ tells us to find the sum.

   The question is asking for the sum of the values of ‍$3-n$ from ‍$n = 0$ to ‍$n = 2$.
   

   Evaluating

   $\begin{aligned} \large\displaystyle\sum\limits_{n=0}^{2 }{({-n})}&= (-0) + (-1) + (-2) \\\\&= 0 + (-1) + (-2) \\\\&= -3\end{aligned}$
   

   The answer

   $\large\displaystyle\sum\limits_{n=0}^{2 }{({-n})}=-3$

   ---

3. What is the question asking for?

   $\sum$ tells us to find the sum.

   The question is asking for the sum of the values of ‍$6x$ from ‍$x = 1$ to ‍$x = 2$.
   

   Evaluating

   ‍$\begin{aligned} \large\displaystyle\sum\limits_{x=1}^{2 }{({6x})}&= (6(1)) + (6(2)) \\\\&= 6 + 12 \\\\&= 18\end{aligned}$

   The answer
   

   ‍$\large\displaystyle\sum\limits_{x=1}^{2 }{({6x})}=18$

   ---

4. What is the question asking for?

   $\sum$ tells us to find the sum.

   The question is asking for the sum of the values of ‍$3-n$ from ‍$n = 0$ to ‍$n = 2$.
   

   Evaluating

   $\begin{aligned} \large\displaystyle\sum\limits_{n=0}^{2 }{({n})}&= (0) + (1) + (2) \\\\&= 0 + 1 + 2 \\\\&= 3\end{aligned}$
   

   The answer

   $\large\displaystyle\sum\limits_{n=0}^{2 }{({n})}=3$