Homework Statement
Prove that for any n \in Z+, the integer (n(n+1)(n+2) + 21) is divisible by 3
Homework Equations
A previously proved lemma (see below)
The Attempt at a Solution
I sort of just need a nudge here. I have a previously proven lemma which states:
If d|a and d|b...
For one of my assignments, I have to write a program to add or subtract complex numbers. I wrote a class, and the problem I am having is that one of my methods isn't returning the data to the calling object. I am going to omit the things in my code that I don't think are pertinent.
int main()...
Thanks, that does make it rather easy.
Just so I am sure I can write this correctly, the justification for equating the two identical inequalities is that k(k-1) > 0 Is that because of the base case starting with n>1 or because induction is on \mathbb{N}
Homework Statement
prove by induction that
\frac{1}{n^2} < \frac{1}{n(n-1)}
Homework Equations
n/a
The Attempt at a Solution
Let
P(n):\frac{1}{n^2} < \frac{1}{n(n-1)}
Since P(1) is undefined, the base case is P(2)
P(2) = \frac{1}{2^2} < \frac{1}{2(2-1)}
P(2) = \frac{1}{4} < \frac{1}{2}...
Another approach similar to mark44's is to use the linspace function but that's just increasing the size of the x vector and letting Matlab handle the size of the partitions.
x = linspace(0,5*pi,50)
y = sin(x)
plot(x,y)
In the linspace function, you can define how many points you would like...
You should just be able to use the SOLVE function in the catalog from the main screen.
I can't remeber what menu it is under, it may be ALGEBRA.
SOLVE(X=2y-y^2,y) {ENTER}
The copy the answer into the Y editor. If there are roots, you have to manually enter each root i.e if you want to look at...