not sure if srs
But your discrete course emphasizes formality.Question is
I'm typing up a super-informal proof right now
A few assumptions are circularity in the proofLet predicate P(n) be ".."
Basis: For n=1, ...
Induction: suppose that k in positive integers
Suppose that P(k) is true
i.e. √1 + √2 + ... + √k ≥ 2/3 k√k
We want to deduce that P(k+1) is true
i.e. √1 + √2 + ... + √k + √(k+1) ≥ 2/3 (k+1)√(k+1)
We have
√1 + √2 + ... + √k + √(k+1)
≥ 2/3 k√k + √(k+1)
Our aim now is to prove that:
 \geq k+1 \\ \\ k\cdot \frac{k}{k+1} \geq k \\ \\ k \geq k+1 \\ \\ 0 \geq 1)
Which line are you referring to?Got it:
 = \frac{2}{3}k\sqrt{k} + \frac{2}{3}\sqrt{k+1} \neq \frac{2}{3}k\sqrt{k} + \sqrt{k+1})
Sorry, was a typo
his first line of latex code
Can you explain everything below "Our aim is to prove".
Ah, he must have edited it.Got it:
I have just edited my post
But you are assuming the truth of the inequality you are trying to prove. Let k = 1, is the inequality true?