Sum to infinity of a G.P. The sum of an infinite geometric series is equal to the value of the first term in the series multiplied by the sum of the ratio o...
Sum to infinity of a G.P.
The sum of an infinite geometric series is equal to the value of the first term in the series multiplied by the sum of the ratio of successive terms. In other words, the sum of a geometric series is equal to the first term * (1/r), where r is the common ratio between successive terms.
Formula:
where:
S is the sum
a is the first term
r is the common ratio
Example:
Consider the geometric series 1, 1/2, 1/4, 1/8, ...
The common ratio between successive terms is 1/2, so the sum of the series can be calculated as:
Another Example:
Consider the geometric series 1, 2, 4, 8, 16.
The common ratio between successive terms is 2, so the sum of the series can be calculated as:
Applications of Sum to Infinity:
Sum to infinity of a geometric series can be used in various applications, such as calculating the sum of infinite geometric series in finance and engineering, finding the area of geometric figures, and solving differential equations