What is sum of exponential?

The sum of an exponential series is given by:

S = a + ar + ar^2 + ... + ar^n-1

Where 'a' is the first term, 'r' is the common ratio and 'n' is the number of terms.

If 'r' is greater than 1, then the sum of the exponential series will be infinite. This is because the terms of the series will keep increasing without any limit as the value of 'n' increases.

If 'r' is between 0 and 1, then the sum of the exponential series can be calculated using the formula:

S = a(1 - r^n)/(1 - r)

This formula is derived by taking the sum of the geometric series:

S = a + ar + ar^2 + ... + ar^n-1

And then multiplying both sides by 'r' and subtracting the result from the original sum. This gives:

S - rS = a - ar^n

Solving for 'S' gives:

S = a(1 - r^n)/(1 - r)

This formula can be used to find the sum of exponential series in various applications, such as in finance, physics, and engineering.