论文标题
谐波和谐波术语数量的界限
Bounds for the Number of Terms of Harmonic Sums
论文作者
论文摘要
本文提供了用$ f $表示的谐波总和表示的条款数量的界限，其条件是从任何任意单位分数$ \ frac {1} {1} {m} $，$ m> 1 $开始，直到另一个单位分数$ \ frac {1} {1} {m+f-1} $ sum比最高的$ sugh yeeger $ q q。此外，我们考虑埃及分数的条款数量，其条款是$ r $，$ r \ geq 1 $的连续倍数，在上述条件下。我们以案例的公式结束论文：$ q = 1 $和$ r = 1 $。
This paper provides bounds for the number of terms, denoted by $f$, of a harmonic sum with the condition that it starts from any arbitrary unit fraction $\frac{1}{m}$, $m > 1$, until another unit fraction $\frac{1}{m+f-1}$ such that the sum is the highest sum less than a particular positive integer $q$. Also, we consider the number of terms of Egyptian fractions whose terms are consecutive multiples of $r$, $r \geq 1$, under the same above condition. We end the paper with a formula for the case: $q=1$ and $r=1$.
