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Lapatulllka [165]
3 years ago
6

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

Mathematics
1 answer:
erastovalidia [21]3 years ago
4 0

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}}

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