I converted the sum into integral format:How did you do this?
And then how do you evaluate that integral? t method seems a little tedious, is there a simpler way?I converted the sum into integral format:
Then I used limiting sum to get:
bump
Isn't this essentially a derivation of the cubic formula? That is famously messy lol.
Theyre all prime numbersbump
A translation of part (ii) is simply "show that no two members of the sequence F_n share a common factor"
Not all of them are; the first several are, but the pattern breaks down after a point.Theyre all prime numbers
For part ii:
You're pretty close though.Edit: Nevermind, I only proved that they are not divisible, I didn't prove that they didn't have a common factor.
Try proving via contradictionFor part ii:
Edit: Nevermind, I only proved that they are not divisible, I didn't prove that they didn't have a common factor.
You're pretty close though.
I'm assuming you would use a similar method but instead of using the numbers F_n, you would use the factors of those integers, and prove that the factors cannot be integers, hence proving they do not share common factors.Try proving via contradiction