How do you write a series in summation notation? This section confused me a lot and I need to know how to do this to apply it to my work.

Question

amistre64 · Answer

that big E is a greek letter S ... for sum

the index of E tell us where to start and stop at

and the rule beside it is, well ... the rule we are summing

amistre64 · Answer

$$\Large \sum_{n=start}^{stop}f(n)$$

anonymous · Answer

where does the k come into play?

amistre64 · Answer

you will have to put that into the context of the author of your material.  the names of a variable are not important

amistre64 · Answer

spose we want to sum of the sequence:  $a_1 + d(n-1)$  from n=3 to k$$\sum_{n=3}^{k}~a_1+d(n-1)$$

anonymous · Answer

Wow this is confusing.. umm could we maybe do an example sequence and apply it? So it's more visual?

amistre64 · Answer

sure

anonymous · Answer

What if the sequence was -1/2 +1/4 -1/6 +1/8 -1/10 +1/12

amistre64 · Answer

the signs are flipping back and forth (alternating)

the denominator is a run of even numbers:  2n

amistre64 · Answer

2(1) = 2
2(6) = 12

so this is a run from n=1 to 6

anonymous · Answer

Why multiply by 1 and 6?

amistre64 · Answer

an even number is of the form:  2n,  we want to know for what values of "n" this series is defined for:  2n = 2,  and 2n = 12; therefore 1 to 6
$$\sum_{n=1}^{6}\frac{(-1)^{n+1}}{2n}$$

amistre64 · Answer

(-1)^n  that +1 is in error

anonymous · Answer

Okay. So that makes some sense. -1^n because it alternates right?

amistre64 · Answer

correct

anonymous · Answer

Okay thank you, I can do these now! c:

amistre64 · Answer

:)  youre welcome

anonymous · Answer

If I were to expand an equation in summation notation, would it be basically working backwards for what we just did?