# Fraction Calculator: 1/2 : 1/3

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

1 + một nửa + 1/3 + 1/4 +.... + 1/n

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 lớn 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 to \$H_n\$ & known as the \$n\$-th Harmonic number.

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

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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!

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

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

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

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