Summation

Summation Notation: Finds the sum of various terms in a sequence. 

This diagram is the summation sign.

The Equation for Summation Notation:

m

∑ ck means C₁+C₂+C₃+….+Cm

k=1

EXAMPLE:

5

∑ (-7+3n) 

n=1

=(-7+3x1) + (-7+3x2) + (-7+3x3) + (-7+3x4) + (-7+3x5)

=(-7+3) + (-7+6) + (-7+9) + (-7+12) + (-7+15) 

=-4-1+2+5+8

=10

Partial Sum: The sum of the first k terms of the sequence.

Formulas for the Partial Sum:

1.

 k

∑ un = k/2 (u₁ + uk)

n=1

2.

k

∑ un = ku₁ + k(k-1)/2  x d

n=1

Using the Calculator to do Partial Sums:

step 1: Press 2nd STAT, highlight MATH and scroll down to number 5: sum( , hit enter

step 2: Press 2nd STAT, highlight OPS and scroll down to number 5: seq( , hit enter

step 3: enter your equation!

EXAMPLE:

A ball is dropped from a hight of 5 feet. It hits the ground and bounces to a hight of 41/2 feet. It continues to bounce, and on each rebound it rises to 9/10 the hight of the previous bounce. 

1. What is the total distance the ball travels through the fifteenth bounce?

       k

5 + ∑ (9) (.9)(n-1)

      n=1

2. What is the command line on your calculator used to calculate the total distance the ball traveled through the fifteenth bounce?

5 + sum(seq(9(.9)(n-1),n,1,14)