Page 14 - Math SL HB Sem 1

SEOUENCE AND SIIRIF,S

SI(;NIA NO'TATION

Consider the series I + 2+4+8+ 16+32
As each term is a power of 2 we can write this series in the form

2o +2' +22 +23 +2' +25 and the general term of this series is 2' .
Using I as a symbol for' the sum of terms' we redefine our series more concisely as

upper
bound
5
l/ (the sum of terms of theform2')
r=2

lower
bound

Example L Write the following series in the sigma notation

(a) I +4+9+ 16 +...+ 100 (b) 1.2+2:3+3.4+...1'19.20

(c)l -x +x' -xtt ... (d)2"4+8-16+...-f128

2-2