Question

Find the sum of the following series.
(shown below)
A. 240
B. 255
C. 210
D. 510

Answer 1

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

Answer 2

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

Answer 3

@phi

Answer 4

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

Answer 5

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)

Answer 6

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

Answer 7

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.
\[\sum_{k=1}^{n}k= \frac{ n(n+1) }{ 2 }\]

Answer 8

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

Answer 9

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

Answer 10

@phi

Answer 11

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?

Answer 12

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