Which infinite geometric series can you NOT find the sum?

Mathematics

1 answer:

Oksanka [162]3 years ago

4 0

Answer: C) 127, 152.4, 182.88, 219.456,...

Step-by-step explanation:

You can only find the sum of an infinite geometric sequence if it converges.

One criterion to see if the series converges is if:

aₙ < aₙ₋₁

This means that, as n increases, the value of the terms decreases.

This means that as n tends to infinity, aₙ tends to zero.

Then we only can find the sum of those series where the terms are decreasing.

in A, B and D the terms are decreasing, then we can find the sum of those 3 series.

Now in the case of C, the terms are increasing, then we can not find the sum of that series.

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Since $\overline{GH} \parallel \overline{DE}$ , by the corresponding angles theorem, $\angle FGH \cong \angle FDE, \angle FHG \cong \angle FED$ . This means $\triangle FGH \sim \triangle FDE$ by AA.

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