Well, my initial concern is that 4n+1 doesn't represent the nth term in the sequence as it should. It only represents it if we start from the notation that the first term is the 0th term in the sequence. It should be 4n-3 instead.
And he's made it clear we don't include 0 in the natural...
After much deliberation with another friend of mine, we came to this conclusion:
If we denote the 1st term by n=0, the 2nd term by n=1 and so on we can use
4n+1 = (n+1)(2n+1)
4(0)+1 = 1 (0+1)(2(0)+1) = 1
and so on, we can see it works
But he explicitly defined in class that in our class...
Homework Statement
Given the sequence 1+5+9+...+(4n+1)
Find the sum of the sequence and then prove that it holds for all natural numbers using induction.
Homework Equations
Just induction, that we solve it using induction and, according to the teacher, by trial and error.
Induction...
Homework Statement
*Sorry I could not get the math symbols to work properly so I did it by hand. I hope this isn't too much trouble.
Prove:
| sqrt( x ) - sqrt( y ) | <= | sqrt ( x - y ) |
for x, y >= 0
Hint: Treat the cases x >= y and x <= y separately.
I am new to proofs and we can't use...