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Bookmark or Share- Proof that $n^3+2n$ is divisible by $3$Basis Step: If n = 0, then n3 + 2n = 03 + 2 × 0 = 0. So it is divisible by 3. Induction: Assume that for an arbitrary natural number n, n3 + 2n is divisible by 3. Induction Hypothesis: To prove this for n + 1, first try to express (n + 1)3 + 2(n + 1) in terms of n3 + 2n and use the induction hypothesis. Got it.
- What is infinity divided by infinity? - Mathematics Stack ExchangeThis webpage discusses the concept of dividing infinity by infinity in mathematics and explores various perspectives on the topic.
- calculus - Why does $1/x$ diverge? - Mathematics Stack Exchange1. 1 x 1 x converges to 0 0 as x → ∞ x → ∞. The OP probably won't see this comment anyway, as they have not logged in recently. The posted answers are correct, and another way to illustrate that the above reasoning (posted in the question) is not, is to consider 1+x x 1 + x x instead. Again we are "adding smaller and smaller numbers ...
- Calculus proof for the area of a circle - Mathematics Stack ExchangeA ′ (r) = 2πr(∗) Intuitively, the rate of change of the area of the circle is the circumference. Formally. A ′ (r) = lim Δr → 0A(r + Δr) − A(r) Δr. Now, geometrically it is pretty clear (but not really easy to prove mathematically) that the area of a corona between circles satisfies.
- Good book for self study of a First Course in Real AnalysisFor self-study, I'm a big fan of Strichartz's book "The way of analysis". It's much less austere than most books, though some people think that it is a bit too discursive.
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