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13 July, 13:15

Which geometric series converges?

0.02+0.02+0.02+0.02 + ...

4+0.08 + 0.0016+0.000032+

4+80 + 1.600 + 32,000+.

0.02+0.04+0.08+0.16+.

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  1. 13 July, 14:41
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    4+0.08 + 0.0016+0.000032 + ...

    Step-by-step explanation:

    a+ar+ar²+ar³+ar⁴+ ...

    the geometric series converges if |r| < 1

    The geometric series converges:

    4+0.08 + 0.0016+0.000032 + ...

    0.08=4*0.02

    0.0016=4 * (0.02) ²

    0.000032=4 * (0.02) ³

    r=0.02<1
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