Question

How is the sum expressed in sigma notation? 1/64+1/16+1/4+1+4

Answer 1

Answer:

The given series in sigma notation is

$\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4=\sum\limits_{i=1}^{5}\frac{1}{4^{4-i}}$

Step-by-step explanation:

Given series is $\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4$

To that given sum expressed in sigma notation :

The given series in sigma notation is

$\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4=\sum\limits_{i=1}^{5}\frac{1}{4^{4-i}}$

Now check the sigma notation is correct or not:

$\sum\limits_{i=1}^{5}\frac{1}{4^{4-i}}=\frac{1}{4^{4-1}}+\frac{1}{4^{4-2}}+\frac{1}{4^{4-3}}+\frac{1}{4^{4-4}}+\frac{1}{4^{4-5}}$

$=\frac{1}{4^3}+\frac{1}{4^2}+\frac{1}{4^1}+\frac{1}{4^0}+\frac{1}{4^{-1}}$

$=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+\frac{1}{1}+4$

$=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4$

Therefore  $\sum\limits_{i-1}^{5}\frac{1}{4^{4-i}}=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4$

Therefore our answer is correct.

The given series in sigma notation is

$\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4=\sum\limits_{i=1}^{5}\frac{1}{4^{4-i}}$