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a) \sum\limits_{r=4}^8 2^r=2^4+2^5+2^6+2^7+2^8 
 


b) (i) Recognize a Growth Pattern
 
a=2^4 , r=2 , n=22
 
\sum\limits_{r=4}^{25} 2^r is a Finite Geometric Series

Use sum of a geometric series formula
 
S_n=\frac{a(r^n-1)}{r-1}
 
S_{22}=\frac{2^4(2^{22}-1)}{2-1}
 
S_{22}=67108848

(ii) Infinite Growth Pattern and r\geq1

Explanations

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