11-4 INTRO TO SERIES DEFINITION A SERIES IS THE SUM OF THE TERMS OF A SEQUENCE. SEQUENCE VS. SERIES 2, 4, 8, … …

N TH PARTIAL SUM THE N TH PARTIAL SUM IS THE SUM OF THE FIRST N TERMS OF THAT SERIES. S N = SUM OF THE FIRST N TERMS

SIGMA NOTATION New notation: ∑  sigma = the sum of upper limit  lower limit  t n FORMULA = = 36

TOO EVALUATE THE EXPRESSION : 3(1) + 3(2) + 3(3) + 3(4) = = 30

EX 2) EVALUATE THE EXPRESSION = (-1) 1 (1+2)+ (-1) 2 (2+2)+ (-1) 3 (3+2) = (-1)(3) + (1)(4)+ (-1)(5) = – – 5 = -4

SIGMA NOTATION WE WANT: WHERE T K IS THE FORMULA TO FIND THE VALUE OF THE N TH TERM. ARITHMETIC: T K = T 1 + (N-1)D GEOMETRIC: T K = T 1 (R) N-1

HOW TO WRITE SIGMA NOTATION WRITE S N USING SIGMA NOTATION EXAMPLE:  S 30 FOR …  IS THE SERIES ARITHMETIC, GEOMETRIC, OR NEITHER? NEITHER!!!!!

SIGMA NOTATION LOOK FOR A PATTERN FOR T K S 30 FOR … T K = K 3 SO, OUR ANSWER IS:

t n = 10 + (n – 1)(5) EX USE SIGMA NOTATION TO WRITE THE SERIES … t n = n – 5 = 5n + 5 Find upper limit:(what term # is 100) t n = 5n + 5  100 = 5n + 5  19 = n Arithmeticd = 5t 1 = 10

Series is geometric!! t n = t 1 (r) n-1 EX USE SIGMA NOTATION TO WRITE THE SERIES t 1 = 1 r = - 1/3How did we get r? Check it!!!

HOMEWORK PG Q1-10 #1 – 35 ODD