# Tagged Questions

For questions about mathematical induction, a method of mathematical proof. Mathematical induction generally proceeds by proving a statement for some integer, called the *base case*, and then proving that if it holds for one integer then it holds for the next integer. This tag is primarily meant ...

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### Using 4-cent and 11-cent stamps for postage (induction)

I was wondering how many base cases are needed and when to stop (in general). For example, I have 4-cent and 11-cent stamps and I need to determine the amount of postage I can make, the cases I have ...
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### Induction problem for $U_{n+1}(x) = 2x U_n(x) - U_{n-1}(x),$ what can be assumed?
I have this straightforward induction problem that perhaps I am over thinking at this time of the morning. Here it is: $U_1(x) = 1, \; U_2(x) = 2x, \; U_{n+1}(x) = 2x U_n(x) - U_{n-1}(x).$ Prove ...
There’s a method of proving inequalities over some interval of real numbers using differentiation. For instance to prove that $x-\log(1+x) \geqslant 0$ whenever $x \geqslant 0$ we can differentiate ...