b. Find a formula for the nth partial sum of the infinite series.

Use the formula to find the next four partial sums , and of the infinite series.

(Type integers or simplified fractions.)

Ask by Herrera Fleming. in the United States

Mar 30,2025

Question

b. Find a formula for the nth partial sum of the infinite series.

Use the formula to find the next four partial sums , and of the infinite series.

(Type integers or simplified fractions.)

Ask by Herrera Fleming. in the United States

Mar 30,2025

UpStudy AI · Accepted Answer

We are given the formula for the $$ n $$th partial sum:

$$
S_{n} = 1-\frac{1}{2^{n}}, \quad n \geq 1.
$$

Now, we find the next four partial sums by substituting $$ n=5, 6, 7, $$ and $$ 8 $$.

1. For $$ n=5 $$:

$$
S_{5} = 1-\frac{1}{2^{5}} = 1-\frac{1}{32} = \frac{31}{32}.
$$

2. For $$ n=6 $$:

$$
S_{6} = 1-\frac{1}{2^{6}} = 1-\frac{1}{64} = \frac{63}{64}.
$$

3. For $$ n=7 $$:

$$
S_{7} = 1-\frac{1}{2^{7}} = 1-\frac{1}{128} = \frac{127}{128}.
$$

4. For $$ n=8 $$:

$$
S_{8} = 1-\frac{1}{2^{8}} = 1-\frac{1}{256} = \frac{255}{256}.
$$

Thus, the values are:

$$ S_{5}=\frac{31}{32}, \quad S_{6}=\frac{63}{64}, \quad S_{7}=\frac{127}{128}, \quad S_{8}=\frac{255}{256}. $$
$$ S_{5}=\frac{31}{32}, \quad S_{6}=\frac{63}{64}, \quad S_{7}=\frac{127}{128}, \quad S_{8}=\frac{255}{256} $$

b. Find a formula for the nth partial sum of the infinite series.

Use the formula to find the next four partial sums , and of the infinite series.

(Type integers or simplified fractions.)

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b. Find a formula for the nth partial sum of the infinite series. Use the formula to find the next four partial sums , and of the infinite series. (Type integers or simplified fractions.)

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b. Find a formula for the nth partial sum of the infinite series.

Use the formula to find the next four partial sums , and of the infinite series.

(Type integers or simplified fractions.)