maths.free › Real Analysis › Sequences and series › Comparison test
Comparison test
Comparison test can mean:Limit comparison test, a method of testing for the convergence of an infinite series.Direct comparison test, a way of deducing the convergence or divergence of an infinite series or an improper…
Comparison test
Comparison test can mean:
- Limit comparison test, a method of testing for the convergence of an infinite series.
- Direct comparison test, a way of deducing the convergence or divergence of an infinite series or an improper integral.
今度はあなたの番 計算機では解けませんが、計算可能です。下の一つを試してみましょう。もしくは自分で入力してください。
ここで使用された記号
どの記号をタップしても、定義、画像、それぞれの文字の意味が表示されます。
よくある質問
What is the ε, δ definition actually saying?
That you can make the output as close to the limit as anyone demands (within ε) by keeping the input close enough (within δ). It replaces "approaches" with a challenge-and-response that can be checked.
Why does the harmonic series diverge when its terms go to zero?
Because the terms shrink too slowly: group them as 1/3 + 1/4 > 1/2, 1/5 + … + 1/8 > 1/2, and so on: infinitely many halves.
Parts of this page are adapted from Wikipedia (CC BY-SA 4.0). ここでは要約して説明し直しています。誤りは私たちの責任です。
More in Real Analysis
Sequences and their limitsConvergence of seriesImproper integralsTaylor approximation and errorFunctions of a complex variableContinuity and differentiability, rigorouslySequences of functions and uniform convergence