Determine whether the series is convergent or divergent. If it is convergent, find its sum.
Whether the series is convergent or divergent and obtain the sum if the series is convergent.
The series is convergent to the sum
The series is
The geometric series
∑n=1∞arn−1 (or) a+ar+ar2+⋯
is convergent if
and its sum is
, where a is the first term and r is the common ratio of the series.
The given series can be written as follows,
Here, the first term of the series is
and the common ratio of the series is,
The absolute value of r is,
and by using Result stated above, the series
Obtain the sum of the series when
a=sin100 and r=sin100
Thus, the sum of the series is
Therefore, the series is convergent to the sum