N=1, ∑ 1/n=1000 -------> is this calculation possible?

Answer 1

This is the logarithm series expansion.
thus log x = 1000
=> x = e^1000

Answer 2

If you want to get really technical, you used capital N versus lower case n:

N may = 1, but what does n =? (1/1000)

If so, this could be possible.

It may also be possible if you are talking conversions, like 1km = 1000 meters, etc...

It all depends on how you define the question: 1 bacteria per one mutation may produce 1000 new types of bacteria.

1 neuton of atomic structure per neutron may produce 1000 joules of energy per some kind of reaction, and so on...

Answer 3

Down below I answered this one way (see below), however, after rereading your question, I thought that you might be asking:
"for which n does 1/1 + 1/2 + ... + 1/n = 1000?"

If this is the case, then you can use the fact that the sum 1/1 + 1/2 + ... + 1/n grows like ln(n) to see that the n which satisfies 1/1 + 1/2 + ... + 1/n = 1000, is approximately e^1000.

I hope one of the responses was what you wanted...


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Prior Answer
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The sum 1/1 + 1/2 + ... + 1/n goes to infinity. However, the sum (1/1 + 1/2 + ... + 1/n) - ln(n) goes to 0.5772... (called the Euler-Mascheroni constant).

The upshot of this, is while there is no nice closed form for the sum 1/1 + 1/2 + ... + 1/1000, it is approximately ln(1000) + 0.5772 = 7.485...

Source(s):

http://en.wikipedia.org/wiki/euler-masch...

Answer 4

I dont think so, its kinda self explanatory.