Question

Summation notation help? One problem. Will give medal!
It says for each sum I need to find the number of terms, the first term, the last term, and to evaluate the sum.
On top of the sigma is 8, under it is n=1, and to the right is 2n/3. I know the number of terms is 8. How do I find the rest.

Answer 1

\[
\sum_{n=1}^{8}\frac{2n}3 = \frac{2(1)}{3} + \frac{2(2)}{3} + \frac{2(3)}{3} +\ldots + \frac{2(7)}{3} + \frac{2(8)}{3}
\]

Answer 2

\[
=(1+2+3+4+5+6+7+8)\times \frac{2}{3}
\]

Answer 3

36*(2/3)=24. That's the sum evaluated?

Answer 4

@wio

Answer 5

Yes, that is correct.

Answer 6

\[\sum _{n=1}^8 k n=k \sum _{n=1}^8 n\]is the property of sums that @wio used

Answer 7

and \[\sum _{n=1}^8 n=\frac{n(n+1)}{2} = \frac{8*9}{2} = 36\]

Answer 8

Thanks so much @whpalmer4