Find the sum of the geometric series.
10
1. Ó 5(2)^i - 1
i= 1
12
2. Ó 8(3/2)^i - 1
i= 1
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Still not showing it. It's in the form of an E.
To find the sum of a geometric series, you can use the formula:
S = a(1 - r^n) / (1 - r)
where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
Let's use this formula to find the sum of the given geometric series:
1. Ó 5(2)^i - 1
i= 1
In this series, the first term (a) is 5, and the common ratio (r) is 2. We need to find the sum of the series up to n = 10.
Using the formula:
S = 5(1 - 2^10) / (1 - 2)
Simplifying further:
S = 5(1 - 1024) / (-1)
S = 5(-1023) / (-1)
S = -5115
So, the sum of the first 10 terms of the given geometric series is -5115.
Now, let's move on to the second question:
2. Ó 8(3/2)^i - 1
i= 1
In this series, the first term (a) is 8, and the common ratio (r) is 3/2. We need to find the sum of the series up to n = 12.
Using the formula:
S = 8(1 - (3/2)^12) / (1 - 3/2)
Simplifying further:
S = 8(1 - (531441/4096)) / (1/2)
S = 8((4096 - 531441) / 4096) / (1/2)
S = (8(4096 - 531441) / 4096) * (2/1)
S = (8 * (-527345)) / 4096
S = -853480 / 512
S = -1669.53125
So, the sum of the first 12 terms of the second geometric series is approximately -1669.53125.