How bởi I calculate this sum in terms of "n"?I know this is a harmonic progression, but I can"t find how to lớn calculate the summation of it. Also, is it an expansion of any magmareport.netematical function?

1 + 50% + 1/3 + 1/4 +.... + 1/n

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There is no simple closed form. But a rough estimate is given by

$$sum_r=1^n frac1r approx int_1^n fracdxx = log n $$

So as a ball park estimate, you know that the sum is roughly $log n$. For more precise estimate you can refer to Euler"s Constant.

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There is no simple expression for it.

But it is encountered so often that it is usually abbreviated khổng lồ $H_n$ và known as the $n$-th Harmonic number.

There are various approximations and other relations which you can find in Wikipedia under Harmonic Number or in the question Jose Santos referenced in the comments.

For example, $$H_n=G_n-(n+1)lfloorfracG_nn+1 floor$$ where $$G_n=fracn+(n+1)!choose n-1(n+1)!$$

But that kind of thing is more of a curiosity than a useful expression!


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One can write$$1+frac12+frac13+cdots+frac1n=gamma+psi(n+1)$$where $gamma$ is Euler"s constant & $psi$ is the digamma function.

Xem thêm: Truyện Sơn Tinh, Thủy Tinh Được Gắn Với Thời Đại Nào Trong Lịch Sử Việt Nam

Of course, one reason for creating the digamma function is to make formulaelike this true.


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how lớn find a sum of numbers in a sequence when some intermediate terms are not taken in to consideration?
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