Find the sum to infinity of the series 1+1/2+1/4+1/8+......
To find the sum to infinity of the series 1+1/2+1/4+1/8+......, we can use the formula for the sum of an infinite geometric series.
The formula for the sum S of an infinite geometric series with a first term a and a common ratio r (where -1 < r < 1) is given by:
S = a / (1 - r)
In this series, the first term a is 1 and the common ratio r is 1/2.
Therefore, substituting these values into the formula for the sum of an infinite geometric series, we get:
S = 1 / (1 - 1/2)
Simplifying this expression, we have:
S = 1 / (1/2)
Dividing 1 by 1/2 is the same as multiplying 1 by 2/1, giving us:
S = 2
Hence, the sum to infinity of the series 1+1/2+1/4+1/8+...... is equal to 2.