Tagged Questions
5
votes
4answers
189 views
Prove the following identity
I am having some trouble proving following identity without use of induction, with which it is trivial.
$$\sum_{n=1}^{m}\frac{1}{n(n+1)(n+2)}=\frac{1}{4}-\frac{1}{2(m+1)(m+2)}$$
I did expand the ...
2
votes
2answers
916 views
How can you prove the Nested Interval(s) Theorem in $\mathbb R$ without reference to the least upper bound property?
Claim: a nested sequence of closed bounded intervals in $\mathbb R$ has nonempty intersection.
A textbook provides a proof using the least upper bound property of the real numbers, but adds an aside ...
3
votes
2answers
232 views
Regarding a proof involving geometric series
Someone asked this question about how many ways there are to prove $0.999\dots = 1$ and I posted this:
$$ 0.99999 \dots = \sum_{k = 1}^\infty \frac{9}{10^k} = 9 \sum_{k = 1}^\infty \frac{1}{10^k} = ...
