Hello, I need to verify my answer:
#Induction Question
sly flax
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knotty oxide
Hello, I need to verify my answer:
correct idea, however you cant start with what you're trying to prove
so the fact you started with $x_{n+1}<4$ then showed you get $9<16$ isnt technically a proof.
lament fossilBOT
Omegabet_
knotty oxide
you can write the proof just as showing $1+2x_n<16$ by the IH, to which the $n+1$ case follows
lament fossilBOT
Omegabet_
sly flax
Oh i see
@knotty oxide so do I just rewrite the first step and I should be good to go right
like from IH i use get it to 9 and then just take sqrt of it
knotty oxide
yes
by the IH $x_n<4\implies 1+2x_n<9<16\implies x_{n+1}=\sqrt{1+2x_n}<\sqrt{16}=4$
lament fossilBOT
Omegabet_
knotty oxide
which technically you also need to prove $x_n\geq 0$, but that's obvious
lament fossilBOT
Omegabet_
sly flax
by the IH $x_n<4\implies 1+2xn<9\implies x{n+1}=\sqrt{1+2x_n}<\sqrt{9}=3$
lament fossilBOT
Laplace
knotty oxide
again, your base case started with what you want to prove
just compute 7! and 3^7 seperately, then state "since 7! > 3^7, the base case is true"
sly flax
just compute 7! and 3^7 seperately, then state "since 7! > 3^7, the base case is...
Ahhh ok I need to fix this issue then I dont want to loose grades in finals - point noted
knotty oxide
I also dont fully know what your argument for the n+1 is
cause you used $3^n>n!$ for some reason
lament fossilBOT
Omegabet_
knotty oxide
which is ofc false
sly flax
**Omegabet\_**
which line did i use this?
knotty oxide
going from (n+1)! > 3^n(n+1) to 3^n(n+1)>3^n*3
or you did something unclear
just prove $3^n(n+1)>3^{n+1}$, then the statement follows since you had $(n+1)!>3^n(n+1)$
lament fossilBOT
Omegabet_
sly flax
**Omegabet\_**
yah did the prove $3^n(n+1)>3^{n+1}$ since you can rewrite it as $3^n(n+1)>3^n*3$
lament fossilBOT
Laplace
knotty oxide
that;s the proof, yes
sly flax
and remove 3^n
knotty oxide
explain why n+1>3
sly flax
n >= 7
sly flax
I wrote that here in the second last line