Pregunta
2.1 Given:
For which values of
will the series converge? Show working details.
For which values of
Ask by Griffin Warner. in South Africa
Mar 14,2025
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Respuesta verificada por el tutor
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The series converges for
values between -2 and 2.
Solución

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Como
The Deep Dive
The given series is an infinite series expressed as
. We can see that it can be rewritten in summation notation as:
This is a power series where each term is of the form
with
. We can determine the convergence of this series using the ratio test.
Using the ratio test, we calculate the limit:
Here,
and
. Therefore:
We take the limit:
For the series to converge, we need
:
This implies:
Thus, the series converges for values of
in the interval:
In conclusion, the series converges for
in the range
.

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