Lesson 18 - Infinite Sum & Sigma

Infinite Sum:

Formula:
S=  a   
     1- r

Example 1:
S10 = 64(1 - 0.5 ^10)     =  127.88              S20= 64(1 - 0.5 ^20)    = 127.99
                 1 - 0.5                                                          1 - 0.5

S99 = 64(1 - 0.5 ^99)    =  128                    S1000 = 64(1 - 0.5 ^1000)     = 128
                  1 - 0.5                                                             1 - 0.5

S ∞ exist only if r is a "fraction" r < 1   r > -1  r cannot = 0  

Sigma:
Formula:
  5                                      Sub 2

∑  2(-3) ^k-1                 2(-3) ^ 2-1       

k = 2                                    -6                      

5= the terms

k=2 : input term        2(-3) ^ k-1: formula

sub numbers all the way to 5  than add all numbers together or use the infinite sum formula.