Help. I need hard induction questions to help myself get better at proof by induction. And please send me multiple. It's hard to find on the internet. So, please. Thx in advance
#Induction Questions
true tartan
real valleyBOT
Help. I need hard induction questions to help myself get better at proof by indu...
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exotic lynx
how hard is “hard”
exotic lynx
that doesn’t seem too bad
true tartan
you get it?
exotic lynx
you’ve proven the $\frac1{1\cdot 2}+\frac1{2 \cdot 3} + \frac1{3 \cdot 4}…$ thing right
hot tokenBOT
Melon B
exotic lynx
prove that $\frac1{1\cdot 2}+\frac1{2 \cdot 3} + \frac1{3 \cdot 4} + … = 1$
hot tokenBOT
Melon B
true tartan
by induction
exotic lynx
an easier version of this that makes the induction slightly more obvious:
prove that $\frac1{1\cdot 2}+\frac1{2 \cdot 3} + \frac1{3 \cdot 4} + … + \frac1{(n-1) \cdot n} = 1 - \frac1n$
hot tokenBOT
Melon B
true tartan
ok cool
exotic lynx
**Melon B**
so the above result follows from this one, and this is a pretty classic induction q
not very hard though so idk if it’s what you want
bright socket
@true tartan by any chance are you doing a level maths
true tartan
year 12
bright socket
year 12
anyhow theres this really good website called MadAs Maths where you can get questions for a level pure and further core maths
exotic lynx
I also had one that’s a bit more combinatorial:
Kevin is climbing a set of n stairs, taking either one or two steps at a time. Find the number of ways he can climb these stairs.
bright socket
so i reccomend going there
true tartan
ok
exotic lynx
I also had one that’s a bit more combinatorial:
> Kevin is climbing a set of n s...
the thing with induction questions is that half the issue is bashing small cases to find the answer and the other half is actually proving it using induction
true tartan
4 unit extension 2 math
bright socket
4 unit extension 2 math
wait aus??
exotic lynx
I’ve got friends who are doing 4u
exotic lynx
isn’t it the holidays though bro’s already grinding
bright socket
isn’t it the holidays though bro’s already grinding
locked in for exams 👺
exotic lynx
do u eat marmite
you mean vegemite 💀 or is this some aus thing I’m too sheltered to know about
exotic lynx
locked in for exams 👺
that’s crazy
it’s legit the start of the year and bro’s grinding
wish I could be that locked in
bright socket
you mean vegemite 💀 or is this some aus thing I’m too sheltered to know about
mb marmite is the british version
bright socket
nah i live in uk
bright socket
do you eat beans on toast
hell no that shi taste bland
true tartan
do u eat marmite
I wish
true tartan
you mean vegemite 💀 or is this some aus thing I’m too sheltered to know about
no
i don't eat vegemite
bright socket
ok so induction
exotic lynx
same
bright socket
idk about you
exotic lynx
i don't eat vegemite
did you solve the first q I gave
exotic lynx
also imagine not asking in hsc server
exotic lynx
but all the induction questions i get
nearly all the ones we get in vic are trivial without induction
bright socket
asuume tru for n = 0/1
exotic lynx
take limit as n approaches infinity
what
bright socket
assume true for k
exotic lynx
wait is this still the sum of fractions
bright socket
assume tru for n+k
true tartan
solve it out
bright socket
if tru for n =k
exotic lynx
I also had one that’s a bit more combinatorial:
> Kevin is climbing a set of n s...
try this one lol idk if it’s very useful for 4u
true tartan
that is use algebra
bright socket
then also true for k+1
true tartan
ok
true tartan
I also had one that’s a bit more combinatorial:
> Kevin is climbing a set of n s...
let a be no. of times you climb twice, b be no. of times you climb once, let a = 1,2,3,4,5....some k where n = 2k or n = 2k+1, then arrange that many a's and (k-a) b's in a line
]
which is k choose a
2a+b = n, a,b > 0
set b = n - 2a, n = 2k or 2k+1
for each value of a, do k choose a and add them up
assuming it isn't 1 or 2 stairs
then it's 1 and 2 respectively
wheat oliveBOT
@true tartan