Find the following sum: 1+2+4+8+...+2^k-1

Answer 1

Step 1:

The sequence is .

The first term of the sequence is .

The second term of the sequence is .

Common ratio is .

.

The third term of the sequence is .

Common ratio is .

.

Since the common ration is same, the series is in geometric series.

Step 2:

Sum of the first terms of the geometric series, .

Where is the first term and is the common ratio.

Substitute and in .

.

Solution:

The sum of the series is .