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serious [3.7K]
3 years ago
8

In order for an infinite geometric series to have a sum, the common ration has to be greater than one.

Mathematics
2 answers:
frez [133]3 years ago
7 0

Answer:

  FALSE

Step-by-step explanation:

If the series has a finite sum, the common ratio is less than 1.

ElenaW [278]3 years ago
4 0

Answer:

The statement is false.

Step-by-step explanation:

The sum of a geometric progression is given by

          s_n=\frac{a(r^n-1)}{r-1}

For an infinite GP the sum is given by

          s_\infty =\frac{a}{1-r}

          This equation can only be used when the common ratio is less than 1.

Here the statement is in order for an infinite geometric series to have a sum, the common ration has to be greater than one. This statement is wrong because the sum equation can only be used when the common ratio is less than 1.

The statement is false.

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