#### To determine

**To find:** The value of *c*.

#### Answer

The value of c=ln(910).

#### Explanation

**Given:**

The series is ∑n=0∞enc=10.

**Result used:**

The sum of the geometric series (∑n=1∞arn−1 (or) a+ar+ar2+⋯) is a1−r, where *a* is the first term and *r* is the common ratio of the series.

Consider the series ∑n=0∞enc.

Rewrite the above series and express as follows.

∑n=0∞enc=∑n=0∞(ec)n=(ec)0+(ec)1+(ec)2+(ec)3+⋯=1+(ec)+(ec)2+(ec)3+⋯

Clearly, it is geometric series with the first term of the series is a=1 and the common ratio is r=ec.

Use the Result stated above, the sum of the series is ∑n=0∞enc=11−ec.

Since ∑n=0∞enc=10, 11−ec=10.

Take reciprocal on both sides,

1−ec−1=110−1−ec=−910ec=910

Take natural logarithm on both sides and use the result ln(em)=m,

ln(ec)=ln(910)c=ln(910)

Therefore, the value of c=ln(910).