How to find sum of arithmetic series?

Question

anonymous · Answer

attachment

amistre64 · Answer

first term  plus  last term

times how many terms there are

and divide in half

amistre64 · Answer

and that is not a picture of an arithmetic series

amistre64 · Answer

$$\sum_{1}^{k}a~r^n=a\frac{1-r^{n+1}}{1-r}$$

amistre64 · Answer

well, that a little wrong, the index normally starts at 0, which throws this one off

amistre64 · Answer

S = r + r^2 + ...+r^n
-rS =    -r^2 - ... -r^n - r^(n+1)
----------------------------
1-r : r - r^(n+1)

amistre64 · Answer

$$\sum_{1}^{k}a~r^n=a\frac{r-r^{n+1}}{1-r}$$

anonymous · Answer

It originally did say zero, but someone told me it should be 1 and not 0.

anonymous · Answer

the original problem was on a "find the errors" assignment and it originally was 0. However, someone told me the error in the problem was that it was 0 and not 1.

amistre64 · Answer

$$\sum_{m}^{k}=\sum_{0}^{k}-\sum_{0}^{m-1}$$

amistre64 · Answer

did you change the index?  what is the original problem?

anonymous · Answer

Yes, I changed it. And the original problem is the same as above, except n was = to 0 instead of 1. I was asked to solve that problem.

amistre64 · Answer

ill get this latex code right one of these days
$${\Large\sum_{0}^{k}ar^n=a\frac{1-r^k}{1-r}}$$