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Vocabulary
Complete the chart.
Word  Definition 
________________  the large, stylized capitol E that means, approximately, "the sum of" 
Index  __________________________________________________________ 
________________  the expression being summed in a sigma 
Limits  __________________________________________________________ 
________________  when a series has a limit, and the limit exists 
________________  when a series does not have a limit, or the limit is infinity 
Hypothesis  __________________________________________________________ 
Mathematical induction  __________________________________________________________ 
Partial sum  __________________________________________________________ 
Properties of Sigma
Label the sigma, index, summand, and limit:
.
The above can be read as "find the _____ of the first ______ terms of the series, where the n^{th }term is ____.
What does the sum above add to? __________
True or false: You can factor a coefficient out of a sum. ____________
.
Express the Sum using Sigma Notation:

1+5+9+13+17 
1+12+13+14+...+110
Find the series of numbers indicated and evaluate the summations:

∑n=−1057−43(n−1) 
∑n=−238−2(n−1) 
∑n=−515+43(n−1) 
∑n=164(12)n−1 
∑n=173(−12)n−1 
∑n=111−3(43)n−1
.
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.
Gauss' Formula
Gauss' Formula allows us to add together the first n positive integers:

∑=(n)(n+1)2
.In your own words, describe how Gauss' Formula works. _________________________________________________________________________
Explain how to use your calculator to solve
_________________________________________________________________________
Keep in mind Gauss' Formula can also be written as
.
Calculate the sums of the given series. You may use addition of individual terms or a series sum formula.

∑n=01014−12(n−1) 
−713−673−21+...+373 
2+4+6+...26 
−2−1+0+...+12  The first eight numbers of an arithmetic sequence add up to 604. The next eight numbers added up equal 156. Find the first number and the common difference in the sequence.

The first number in an arithmetic sequence is 80. Find the common difference if we also know that
s9 is eighteen timesa11 
If
an is an arithmetic sequence witha1=1 . Find the second number if we know that the sum of the first five numbers is onefourth of the sum of the next five numbers. 
Given
(an)=78,75,72,69... Finda150 ands150
.
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