9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n"...

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May 14, 2010 9.5 Series Summation Notation: Σ a k k=1 n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1 k=1 5 8 k=5 n=0 n=1 12 ∞ ∞

Transcript of 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n"...

Page 1: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

9.5 Series

Summation Notation:

Σ akk=1

n "the sum of ak from k = 1 to n"

Find the sums.

1. Σ 3k

2. Σ k2

3. Σ cos (nπ)

4. Σ sin (nπ)

5. Σ 310k

k=1

k=1

5

8

k=5

n=0

n=1

12

∞

∞

Page 2: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

The Sum of a Finite Arithmetic Sequence

S = n2 (a + a )

Ex. Add.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

Page 3: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

1. Find the sum of :

1+3+5+7+9+11+13+15+17+19

Page 4: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

2. Find the sum of the integers from 1 to 100.

Page 5: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

3. An auditorium has 20 rows of seats. There are 20 seats in the 1st row, 21 seats in the 2nd, 22 in the 3rd and so on. How many total seats?

Page 6: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

5. Find the sum and write in sigma notation.

3 + 8 + 13 + ... + 98

Page 7: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

4. Find the 150th partial sum of 5, 16, 27, 38, 49 , ..

Page 8: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

Sum of a Finite Geometric Sequence

S = a + a r + a r + a r + a r + ... + a r

rS =

S - rS =

Page 9: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

1. Find the sum of the first 10 terms.

100, 20, 4, ...

Page 10: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

2. Find the sum.

1 + 5 + 25 + ... + 15,625

Page 11: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

The Sum of an Infinite Geometric Series

S = a 1 - r

Page 12: 9.5 Series Summation Notation...Summation Notation: Σ a k=1 k n "the sum of a k from k = 1 to n" Find the sums. 1. Σ 3k 2. Σ k 2 3. Σ cos (nπ) 4. Σ sin (nπ) 5. Σ 3 10 k k=1

May 14, 2010

Determine whether the infinite geometric series converges. If it does, find its sum.

1. 1/48 + 1/16 + 3/16 + 9/16 + ...

2.


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