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Determine whether the following infinite geometric series diverges or converges. If the series converges, state the sum.8 + 32 + 128+ • • •

Determine Whether The Following Infinite Geometric Series Diverges Or Converges If The Series Converges State The Sum8 32 128 class=

Sagot :

A geometric series is given by

[tex]\sum ^{\infty}_{n\mathop=0}a_1(r)^{n-1}[/tex]

Where a1 represents the first term and r represents the common ratio.

The first term of our series is 8, and to find the common ratio we just need to divide one term by the previous one.

[tex]\frac{32}{8}=4[/tex]

Our geometric series is

[tex]\sum ^{\infty}_{n\mathop{=}0}8(4)^{n-1}[/tex]

A geometric series converges if and only if

[tex]-1the common ratio is within this range. Since 4 is not on this range, this series diverges.
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