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## Nerdgirl one year ago Find the sum of the following series. (shown below) A. 240 B. 255 C. 210 D. 510

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1. Nerdgirl

|dw:1434376110688:dw|

2. Nerdgirl

@aloud that's not one of my answers @phi PLEASE HELP!

3. Nerdgirl

no you ditz it's not one of them don't you get it?! it's not one of the answer choices!

4. Nerdgirl

@phi

5. phi

rewrite the problem $\sum_{1}^{15}(2n+1)= 2\sum_{1}^{15}n+\sum_{1}^{15}1$

6. phi

There is a formula to add up the numbers from 1 to n do you know it? and the second sum means add up 15 1's (which hopefully you know how to do)

7. Nerdgirl

Mmm.... what would you say if I said I knew it but I couldn't remember it? :p

8. phi

Gauss (famous mathematician), when a young kid in school was given the problem of adding up the numbers from 1 to 100, and he (clever fellow) saw a way to do it quickly. $\sum_{k=1}^{n}k= \frac{ n(n+1) }{ 2 }$

9. phi

your problem has n=15 so use that formula with n=15 and n+1 = 16

10. Nerdgirl

so it would be 15 (greek symbol) k=1 (1) = 15 (16)/2? @phi

11. Nerdgirl

@phi

12. phi

the sum of the numbers 1 to 15 is 15*16/2 = 15*8= 120 $\sum_{1}^{15}(2n+1)= 2\sum_{n=1}^{15}n+\sum_{n=1}^{15}1 \\ = 2(120) + \sum_{1}^{15}1$ the sum of 15 ones is 15*1= 15 thus $\sum_{1}^{15}(2n+1)= 2\sum_{n=1}^{15}n+\sum_{n=1}^{15}1 \\ = 2(120) + 15$ can you finish?

13. Nerdgirl

OMG ILY THANK YOU!!!!!!!!!!!

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