9.1 Infinite Series; Geometric Series

Convergence versus Divergence of Infinite Series

An infinite series with the partial sum is said to converge with sum S if S is a finite number such that and in this case, we write .

The series is said to diverge if does not exist as a finite number.

Use Summation notation to write the given series in compact form.

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Find the fourth partial sum of the given series

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Telescoping Series

Find the sum of the given telescoping series.

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Sum and Multiple Rules for Convergent Infinite Series

If the series and converge, then the following converge as indicated

Geometric Series

The geometric series , with common ratio, r,

converges if with sum

Otherwise (), the series diverges

Determine whether the given geometric series, converges, and if so, find its sum.

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