Respuesta :
Answer:
The given series in sigma notation is
[tex]\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4=\sum\limits_{i=1}^{5}\frac{1}{4^{4-i}}[/tex]
Step-by-step explanation:
Given series is [tex]\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]
To that given sum expressed in sigma notation :
The given series in sigma notation is
[tex]\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4=\sum\limits_{i=1}^{5}\frac{1}{4^{4-i}}[/tex]
Now check the sigma notation is correct or not:
[tex]\sum\limits_{i=1}^{5}\frac{1}{4^{4-i}}=\frac{1}{4^{4-1}}+\frac{1}{4^{4-2}}+\frac{1}{4^{4-3}}+\frac{1}{4^{4-4}}+\frac{1}{4^{4-5}}[/tex]
[tex]=\frac{1}{4^3}+\frac{1}{4^2}+\frac{1}{4^1}+\frac{1}{4^0}+\frac{1}{4^{-1}}[/tex]
[tex]=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+\frac{1}{1}+4[/tex]
[tex]=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]
Therefore [tex]\sum\limits_{i-1}^{5}\frac{1}{4^{4-i}}=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]
Therefore our answer is correct.
The given series in sigma notation is
[tex]\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4=\sum\limits_{i=1}^{5}\frac{1}{4^{4-i}}[/tex]
