Arithmetic and Geometric Series and their Sums

I hope everyone had a wonderful break :) I know the past week off was appreciated, and for me, needed. But anyways back to business...

Section thirteen three is basically on the sums of the geometric and arithmetic series. This section, like the rest of the chapter is relatively simple. Some important terms to remember are Finite, which is a certain number, and infinite, which is an unlimited number of terms. There are two formulas; one for each sequence and you simply replace, or substitute the numbers given. Once you have learned to solve these types of problems, it will be easier to solve the more difficult ones.

Sum of arithmetic series :
Sn=n(t1+tn) /2
Sum or geometric series:
Sn=t1(1-r^n)/1-r
Where r is the common ratio and is not equal to one.

Ex. Find the sum of the arithmetic series .
1. S10: t1=3,t10=39
S10=10(3+39)/2
S10=10(42)/2
S10=420/2
S10=210

Ex. Find the sum of the geometric series.
1. Find the sum if the first 50 terms.
2,4,8..
• Because the t50, or the fiftieth term is not given you must go back to section one to find it.
T50=2+(50-1)2
T50=2+(49)2
T50=100
S50=2(1-2^50)/1-50
Finally you just solve to get your answer.
:)