Erdos Borwein Constant Calculator
Free online erdos borwein constant calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
Erdős–Borwein 常数 E = Σ 1/(2ⁿ−1) = 1 + 1/3 + 1/7 + 1/15 + … ≈ 1.606695152415292。它同时等于 Σ d(n)/2ⁿ（除数函数 d(n) 在 2ⁿ 处的生成级数，n=1 起步），把梅森数的倒数与因子个数绑在一起。
Erdős 在 1948 年证明它是无理数，Borwein 给出高效算法。二进制视角：1/(2ⁿ−1) 的二进制展开正是 0.0001001001… 型的循环节，求和即对「自相似位串」计数。
参考值
E = 1.606695152415292（N=60 已达机器精度）
前 5 项 1 + 0.333333 + 0.142857 + 0.0666667 + 0.0322581 = 1.575115
How to use the Erdos Borwein Constant Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Erdos Borwein Constant Calculator free?
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Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-27
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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