$\"\"$

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The series is $\"\"$ .

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The series is in the form of alternating series.

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The series is converges if $\"\"$ and $\"\"$ .

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Here $\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ .

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The approximate sum of the series with an error of less than $\"\"$ .

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If the series is convergence $\"\"$ .

\

$\"\"$

\

Hence $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Therefore,the total number of terms required to approximate sum of the series with an error of less than $\"\"$ are $\"\"$ terms.

\

$\"\"$

\

The total number of terms required to approximate sum of the series with an error of less than $\"\"$ are $\"\"$ terms.