1
vote
2answers
71 views

Is this simple proof about symmetric sums correct?

I'm asked to prove $$x \gt 0, y \gt 0, z \gt 0 \rightarrow$$ $$\left(\frac{x+y}{x+y+z}\right)^\frac{1}{2}+\left(\frac{x+z}{x+y+z}\right)^\frac{1}{2} + \left(\frac{y+z}{x+y+z}\right)^\frac{1}{2} \le ...
1
vote
1answer
141 views

Inequality for the Binomial Theorem

I want to show that $(1+ \frac{1}{k})^k \geq 2$ for say $k \geq 2$. Here is what I have so far: By the Binomial Theorem we know $(1 + x)^k$ for $k \geq 2$ gives us: $1^k + {k\choose 1}1^{k-1}x^1 + ...
3
votes
1answer
366 views

Is $(x+1)^2 = (x+1)^3$ for any $x$?

This is something I've been struggling to understand since the past few days. Let's take an example: Prove/Disprove: $(x+1)^2 = (x+1)^3$ for all real values of $x$. Proof: Let us assume the ...