在這篇論文，我們研究級數的第n 項會趨近於零的遞減正級數，例如:調和級數，的數值收斂性。由於浮點數系統的限制，當我們把級數直接計算且沒有使用額外的策略或計算技巧，級數都會是收斂的。
在這篇論文，我們發展了一個計算級數的部分合的策略，使得級數的收斂性可以被決定。基於這個策略，我們也做了一些數值實驗。以下是決定收斂性的標準。 如果級數的部分合的最後一項的索引大於2 的40 次方，則級數被稱為是數值發散的。

In this thesis, we study on the numerical convergence for decreasing positive series which n-th term approaches to zero, e.g., the harmonic series. According to the precision limitation of the floating point number system, the series is always convergent whenever it is treated straightforwardly without any additional strategy or computation skill.
In this thesis, we develop a strategy for evaluating a partial sum of the target series so that the convergence of the series can be determined. Based on the strategy, we also have some numerical experiments. The criterion for determining the convergence is as follows. If the index of the last term of the partial sum is larger than 2^40, the series is called divergent numerically.

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