Aim: What is this symbol It

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Aim What is this symbol Its Greek
to me!
Do Now
Find the sum of the geometric series.
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Definition of Summation Notation
sum of terms
sigma
When n is a specific number, the sum of a
sequence is called a finite series.
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Summation Notation

The first term of the summation is formed by
substituting the lower limit for the index into
the general term. Each succeeding term of the
summation is formed using successive integral
values of the index, until the upper limit is
reached.
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Properties of Sums
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Model Problems
Find the value of each summation
2(0 1 2 3 4 5 6)
2(21) 42
(2 2)2 (3 2)2 (4 2)2 (5
2)2
02 12 22 32 14
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Model Problems
Rewrite using the summation symbol
2(1) 2(2) 2(3) 2(4) 2(5)
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Regents Questions
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The Sum of an Arithmetic Sequence Series
In an arithmetic series, if a1 is the first term,
n is the number of terms, an is the nth term, and
d is the common difference, then Sn the sum of
the arithmetic series, is given by the
formulas
or
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The nth Term of an Arithmetic Sequence
The nth term of an arithmetic sequence has the
form an dn c where d is the common
difference between consecutive terms of the
sequence and c a1 d
An alternative form of the nth term is
an a1 (n 1)d
Summation and Arithmetic Series
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Regents Questions
Find the partial sum of the following arithmetic
series
115
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The Sum of a Finite Geometric Sequence
The sum of the finite geometric sequence a1,
a1r2, a1r3, a1r4, . . . . a1rn - 1 . . . . with
common ratio r ? 1 is given by
Find the sum of the first eight terms of the
geometric sequence 1, 3, 9, 27, . . .
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The Sum of a Finite Geometric Sequence
r ?
3
a1 a1r a1r2 a1r3 . . . a1r8 - 1

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The Sum of a Finite Geometric Sequence
r ?
3

1(3)7
1 3 9 27 . . .
3280
1 1(3) 1(3)2 1(3)3 . . . .
3280
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Model Problem
a1 10 r -1/2
n 11
How many terms in the series?
starting at i 0, there are 11 terms
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Regents Questions
Find the sum of the following geometric series.
4368
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The Sum of a Infinite Geometric Sequence
If r lt 1, then the infinite geometric sequence
a1, a1r2, a1r3, a1r4, . . . . a1rn - 1 . . .
has the sum
4 4(0.6) 4(0.6)2 4(0.6)3 . .
a1 4 and r 0.6 - (r lt 1)
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Model Problem
Find the sum of 3 0.3 0.03 0.003 . . .
a1 3 and r ?
0.1
3 3(0.1) 3(0.1)2 3(0.1)3 . . .
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Model Problem
Express the series in sigma notation and find the
sum. 54 18 6 2 2/3 2/9
728/9
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Model Problem
Find the sum of
a1 4(0.3)1 1.2
n 12
r 0.3
? 1.714