How do you find the sum of #Sigma 2i^2# where i is [0,5]?

Question

Elijah Abram · Accepted Answer

# sum_(i=0)^5 2i^2 = 110 #

We seek: # sum_(i=0)^5 2i^2 = 2 .0^2 + 2 .1^2 + 2 .2^2 + 2 .3^2 + 2 .4^2 + 2 .5^2 # # \ \ \ \ \ \ \ \ \ \ \ = 2 (0^2 + 1^2 + 2^2 + 3^2 + 4^2 + 5^2 ) # # \ \ \ \ \ \ \ \ \ \ \ = 2 (0 + 1 + 4+ 9 + 16 + 25 ) # # \ \ \ \ \ \ \ \ \ \ \ = 2 (55 ) # # \ \ \ \ \ \ \ \ \ \ \ = 110 #

Ezekiel Alexander · Answer

undefined To find the sum of the series represented by the sigma notation $ \sum_{i=0}^{5} 2i^2 $, you follow these steps:

1. **Understand the Sigma Notation**: The given notation means that you are summing the values of $2i^2$ for every integer $i$ starting from 0 up to 5.

2. **Calculate Each Term**: Calculate the value of $2i^2$ for each $i$ in the range [0,5] and then sum these values. The formula $2i^2$ means you square $i$, and then multiply the result by 2.

- For $i = 0$, $2 \times 0^2 = 0$
   - For $i = 1$, $2 \times 1^2 = 2$
   - For $i = 2$, $2 \times 2^2 = 8$
   - For $i = 3$, $2 \times 3^2 = 18$
   - For $i = 4$, $2 \times 4^2 = 32$
   - For $i = 5$, $2 \times 5^2 = 50$

3. **Sum the Results**: Add all the calculated values together.

Let's compute the total sum.The sum of the series represented by $ \Sigma_{i=0}^{5} 2i^2 $ is 110.