calculate the infinite sum of a geometric series with first term 15,000 and common ratio by (1-1/10)
If r=9/10, a0=15000, then
Σ1-∞ ai
=15,000/(1-r)
=150,000
To calculate the infinite sum of a geometric series, we need to use the formula:
S = a / (1 - r),
where:
S: The sum of the infinite geometric series.
a: The first term of the geometric series.
r: The common ratio of the geometric series.
In this case, the first term (a) is 15,000 and the common ratio (r) is 1 - 1/10.
Let's substitute these values into the formula to find the sum (S):
S = 15000 / (1 - (1 - 1/10))
First, simplify the denominator:
S = 15000 / (1 - 9/10)
S = 15000 / (1/10)
Since dividing by 1/10 is the same as multiplying by 10, we have:
S = 15000 * 10
S = 150,000
Therefore, the sum of the infinite geometric series with a first term of 15,000 and a common ratio of (1 - 1/10) is equal to 150,000.