Ivy Do, Christiana Kim, Julia O’Loughin, Tomoki Yagasaki.

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Presentation transcript:

Ivy Do, Christiana Kim, Julia O’Loughin, Tomoki Yagasaki

Summation Notation Study Tip: Summation notation is an instruction to add the terms of a sequence. The upper limit of summation tells you where to end the sum. Summation notation helps you generate the appropriate terms of the sequence prior to finding the actual sum, which may be unclear.

Summation Notation aka Sigma Notation - A convenient notation for the sum of the terms of a finite sequence -Symbol:  (Sigma) n  Upper limit of summation  ai index of summation  i=1  lower limit of summation

4  ( Multiply until this #)  3i i= 2   (start multiplying with this #) (Plug in) = 3(2) + 3(3) + 3(4) (Simplify) = 3 (2+3+4) (Add #’s in Parenthesis) = 3(9) (Mulitiply) =27

Examples Find the Sum: 6  2i 2 i=2 5  (2i+1) i=1 Tips: *Plug in *Work out *Add Tips: *Plug in *Square *Simplify *Solve

Sum Sequence Feature in Calculator Example: #90 page 565 Use a calculator to find the sum: STEPS: 1. Go to List (2 nd -Stat) 2.Move your cursor over to Math 3.Select #5: sum( 4.Go back to List (2 nd -Stat) 5.Move your cursor over to OPS 6.Select #6: seq( 7.Now it should say sum(seq( 8.Enter the problem, be careful with your parenthesis! 9.Use the comma button (above #7) enter K,0,4 and close with 2 parenthesis 4  (-1) k / k! K=0

Properties of Sums

Examples Use the properties of sums to expand: 4  [ (i-1) 2 + (i+1) 3 ] K=0

Examples  Use Sigma Notation to write the sum (1) + 3(2) + 3(3) (9)

Definition of a Series  Consider the infinite sequence a 1, a 2, a 3,... a i … 1. The sum of the first n terms of the sequences is called a finite series or the partial sum of the sequence and is denoted by n a 1 + a 2 +a 3 …….+a n =  a i i=1

2. The sum of all the terms of the infinite sequence is called an infinite series and is denoted by  a 1 + a 2 +a 3 …….+a n =  ai i=1

Examples Find the third partial sum:   4(-1/2) n i=1

Examples Find the sum of the infinite series:   6(1/10) i i=1

 Sigma Notation for Sums  Christiana Kim  Sum Sequence Feature (Graphing)  Julia O’ Loughin  Properties of Sums  Ivy Do  Finding the Sum of Series  Tomoki Yagasaki