Σ 求和（Σ）计算器Summation Calculator (Sigma Notation)

使用说明与常见问题How-to & FAQ

「求和（Σ）计算器」是什么？What is the Summation Calculator (Sigma Notation) tool?

计算 Σ 求和：输入通项表达式（变量 n）和上下限，算出总和，并列出前几项；可识别等差、等比数列求和，适合检查级数作业。Evaluate a sigma-notation sum: enter the general term in n and the lower and upper limits to get the total and the first terms — handy for checking series homework.

如何使用「求和（Σ）计算器」？How do I use the Summation Calculator (Sigma Notation) tool?

在「求和（Σ）计算器」中，填写「通项 f(n)」、「下限」、「上限」等参数，结果会随输入实时计算并显示在下方。In the Summation Calculator (Sigma Notation): Fill in "General term f(n)", "Lower limit", "Upper limit"; results are recalculated instantly as you type.

表达式怎么写？How do I write the term?

用 n（也可用 k 或 i）作变量，支持 + − * / ^、括号、隐式乘法（如 2n）和 sin、sqrt、ln、exp、abs 等函数，例如 1/n^2、(-1)^n/n、2^n。Use n (or k or i) as the variable with + − * / ^, brackets, implicit multiplication like 2n and functions such as sin, sqrt, ln, exp and abs — e.g. 1/n^2, (-1)^n/n or 2^n.

结果精确吗？Is the result exact?

使用双精度浮点数并配合 Kahan-Neumaier 补偿求和，约 15 位有效数字；对极大的整数结果可能有微小舍入。It uses double precision with Kahan–Neumaier compensated summation, about 15 significant digits; very large integer results may round slightly.

能算无穷级数吗？Can it sum an infinite series?

不能直接计算无穷项，但可以用很大的上限观察部分和是否趋于某个值，例如 Σ 1/n² 趋近 π²/6 ≈ 1.6449。Not directly, but a large upper limit shows whether the partial sums settle — Σ 1/n² approaches π²/6 ≈ 1.6449.

计算精度如何？How precise are the results?

「求和（Σ）计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Summation Calculator (Sigma Notation) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「求和（Σ）计算器」免费吗？需要注册吗？Is the Summation Calculator (Sigma Notation) free? Do I need an account?

「求和（Σ）计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Summation Calculator (Sigma Notation) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.