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roygbiv1233
26.07.2019 •
Mathematics
Find the sum of the following infinite sequence: 8, 2, .5, … 1. 10.67 2. 16.67 3. 64 4. 32
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Ответ:
Explanation:
The given series is a geometric series:
8 , 2 , 0.5 , ...... etc
The general formula of the geometric sequence is:
a1 , a1*r , a1*r² , ......
Comparing the general form with the given, we would find that:
a1 = 8
a1 * r = 2
Therefore:
8*r = 2
r = 2/8 = 0.25
We can double check using another term as follows:
a1 = 8
a1*r² = 0.5
8r² = 0.5
r² = 0.5/8 = 0.0625
r = √0.0625 = 0.25
Now, we will get the sum of the sequence as follows:
S =
Hope this helps :)
Ответ: