 #1
mcastillo356
Gold Member
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 TL;DR Summary

It's so a basic question that I feel shame.
I'm still not sure about this solved reasoning that involves inequalities
How do we get ##\epsilon(2p+\epsilon)<\epsilon(2p+1)<2p^2## from ##0<\epsilon<1## and ##\epsilon<\dfrac{2p^2}{2p+1}##?
Answer: As we have ##\epsilon<1##, we've got ##2p+\epsilon<2p+1##; therefore, ## \epsilon(2p+\epsilon)<\epsilon(2p+1) ##;
as we have ##\epsilon<\dfrac{2p^2}{2p+1}##, we also have ##\epsilon(2p+1)<2p^2##. Is the redcoloured argue what I don't understand
Greetings, appreciated PF
Answer: As we have ##\epsilon<1##, we've got ##2p+\epsilon<2p+1##; therefore, ## \epsilon(2p+\epsilon)<\epsilon(2p+1) ##;
as we have ##\epsilon<\dfrac{2p^2}{2p+1}##, we also have ##\epsilon(2p+1)<2p^2##. Is the redcoloured argue what I don't understand
Greetings, appreciated PF