#MAASL00263

a) Use 2 as your starting exponent

3 is the base of all exponents

6 is the maximum exponent

\sum\limits_{r=2}^6 3^r= 3^2+3^3+3^3+3^5+3^6 



b) (i) Recognize a Growth Pattern
 
a=3^2 because 3^1=3

r=2, as described in the sigma notation

n=21: 22-2+1=21. 

Starting at the second term and going up to the 22nd term

Add the 1 due to inclusion of the 2nd term
 
\sum\limits_{r=2}^{22} 3^r is a Finite Geometric Series

Use sum of a geometric series formula
 
S_n=\frac{a(r^n-1)}{r-1}
 
S_{21}=\frac{3^2(2^{21}-1)}{2-1}

S_{21}=\frac{9(2097151)}{1}
 
S_{21}=18874359

(ii) Infinite Growth Pattern and r\geq1

Share the joy with your friends:

Share on facebook
Facebook
Share on twitter
Twitter
Share on reddit
Reddit
Share on whatsapp
WhatsApp
Share on email
Email