How would you do this ? (1 Viewer)

An0nyM0usUseR455 · Mar 21, 2023

I got the RHS of the inequality just dont understand why 1 is less than nth root of n. Should it not be less than or equal to?

Screen Shot 2023-03-21 at 8.21.30 pm.jpg

An0nyM0usUseR455 · Mar 21, 2023

tywebb said:
So to do the actual question:

a.

$\text{Base Step: }$
$2^1=2>1\text{ but in this case I would also check }2^2=4>2\text{ and you will see why in the induction step}$

$\text{Induction Step:}$
$\text{If for }k>1, 2^k>k\text{ then }$
$2^{k+1}=2^k\cdot2>k\cdot2=k+1+k-1>k+1\text{ since }k>1$

Hence by the principle of mathematical induction, for all positive integers $n, 2^n>n$

b.

$2^n>n\ge1\therefore1=\sqrt[1]{1}\le\sqrt[n]{n}<\sqrt[n]{2^n}=2\text{ i.e., }1\le\sqrt[n]{n}<2$

Thanks bro appreciate it !!!

I applied the same steps as u, was just confused why there was no equal sign but I am glad you agree with me !!!

Have a great night

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How would you do this ? (1 Viewer)

An0nyM0usUseR455

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