Patrick G.
asked • 11/14/17Summation division property
3
∑ 2/n
n=1
The answer is 11/3. I know how to find the answer by adding up 2 + 1 + 2/3. But I want to know how to do it by the summation properties. There is a multiplication property that says you can pull out the number but there isn't one for division.
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2 Answers By Expert Tutors
Inactive Tutor answered • 11/14/17
Tutor
New to Wyzant
Student, you can factor out the two so that the thing being summed is 1/n for each value of n. Whatever you get from that summation, don't forget the segregated factor of 2--apply to the summation.
Patrick G.
So this would be:
3
2 ∑ 1/n
n=1
It would still be a summation of a division (1/n). I am only able to find the summation of n by itself which is 3*4/2 = 6. What do I do when it's 1/n ?
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11/14/17
Inactive Tutor answered • 11/14/17
Tutor
New to Wyzant
2 + (2/2) + (2/3) =
3 + (2/3) =
(3 * 3 + 2) / 3 =
11 / 3
Patrick G.
I know how to do it this way. But it would get tedious if the 3 was 300 or 100000. Do you how to do it by the summation properties?
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11/14/17
Inactive Tutor
If you wanted the summation of 1/n for all n values from 1 to infinity, you would be seeking the sum so-called Harmonic Series, but that does not converge. For a finite series, you're left to your own devices.
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11/14/17
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Inactive Tutor
11/14/17