最简真分数加起来到底有多少呢？快来一起算算这个数学小秘密吧！

要计算最简真分数的和，我们需要知道所有可能的真分数。真分数是指分子小于分母的分数，例如1/2、1/3、1/4等。

我们列出所有可能的真分数：

$$\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, \frac{1}{8}, \frac{1}{9}, \frac{1}{10}, \frac{1}{11}, \frac{1}{12}, \frac{1}{13}, \frac{1}{14}, \frac{1}{15}, \frac{1}{16}, \frac{1}{17}, \frac{1}{18}, \frac{1}{19}, \frac{1}{20}, \frac{1}{21}, \frac{1}{22}, \frac{1}{23}, \frac{1}{24}, \frac{1}{25}, \frac{1}{26}, \frac{1}{27}, \frac{1}{28}, \frac{1}{29}, \frac{1}{30}, \frac{1}{31}, \frac{1}{32}, \frac{1}{33}, \frac{1}{34}, \frac{1}{35}, \frac{1}{36}, \frac{1}{37}, \frac{1}{38}, \frac{1}{39}, \frac{1}{40}, \frac{1}{41}, \frac{1}{42}, \frac{1}{43}, \frac{1}{44}, \frac{1}{45}, \frac{1}{46}, \frac{1}{47}, \frac{1}{48}, \frac{1}{49}, \frac{1}{50}, \frac{1}{51}, \frac{1}{52}, \frac{1}{53}, \frac{1}{54}, \frac{1}{55}, \frac{1}{56}, \frac{1}{57}, \frac{1}{58}, \frac{1}{59}, \frac{1}{60}, \frac{1}{61}, \frac{1}{62}, \frac{1}{63}, \frac{1}{64}, \frac{1}{65}, \frac{1}{66}, \frac{1}{67}, \frac{1}{68}, \frac{1}{69}, \frac{1}{70}, \frac{1}{71}, \frac{1}{72}, \frac{1}{73}, \frac{1}{74}, \frac{1}{75}, \frac{1}{76}, \frac{1}{77}, \frac{1}{78}, \frac{1}{79}, \frac{1}{80}, \frac{1}{81}, \frac{1}{82}, \frac{1}{83}, \frac{1}{84}, \frac{1}{85}, \frac{1}{86}, \frac{1}{87}, \frac{1}{88}, \frac{1}{89}, \frac{1}{90}, \frac{1}{91}, \frac{1}{92}, \frac{1}{93}, \frac{1}{94}, \frac{1}{95}, \frac{1}{96}, \frac{1}{97}, \frac{1}{98}, \frac{1}{99} $$

这些分数加起来的总和是：

$$\sum_{i=1}^{99} \frac{1}{i}$$

这个求和没有简单的封闭形式，但可以通过编程或使用数学软件来计算。为了简化计算，我们可以使用对数来估计这个求和的值。我们知道$\ln(n)$是一个关于$n$的函数，其中$n$是正整数。对于$n=99$，我们有：

$$\ln(99) = 99 \cdot \ln(2)$$

因为$\ln(2)$大约是$0.693$，所以：

$$\ln(99) = 99 \cdot 0.693 = 68.577$$

$\sum_{i=1}^{99} \frac{1}{i}$的近似值是：

$$\sum_{i=1}^{99} \frac{1}{i} = e^{68.577} - 1$$

这个结果是一个近似值，实际的数值需要通过计算器或数学软件来得到。