Why is 0≥1? (1 Viewer)

HeroicPandas

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Alright, fresh start... sorry

Beginning from the use of induction hypothesis





Now we need to prove that (time for a discovery)



Subtract 1.5 on both sides



Multiply both sides by 2sqrt(k+1)





Edits:

Actually.. as k>0 and sqrt(k+1)>0, then sqrt(k) - sqrt(k+1)> 0 for LHS >0, so k>k+1, 0>1..................

When does equality occur?
 
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SpiralFlex

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Alright, fresh start... sorry

Beginning from the use of induction hypothesis





Now we need to prove that (time for a discovery)



Subtract 1 on both sides



Multiply both sides by 2sqrt(k+1)





Edits:

Actually.. as k>0 and sqrt(k+1)>0, then sqrt(k) - sqrt(k+1)> 0 for LHS >0, so k>k+1, 0>1..................

When does equality occur?
Counter example k = 1. Read my spoiler.
 

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