- #1
MathematicalPhysicist
Gold Member
- 4,699
- 371
i'm having a problem proving raabe's criteria for convergent sums.
here in planetmath there's a description of it:
http://planetmath.org/encyclopedia/RaabesCriteria.html
i got that the first inequality is correct when mu is smaller than 1.
i got a hint in my test that i should show that {na_(n+1)} is monotonely decreasing, which i did and by another theorem to show c_n=(n-1)a_n-na_(n+1) is convergent which i also did, but i got that
(1-a_(n+1)/a_n)*n=(1-(1-1/n))*n=1>=mu.
where have i gone wrong?
thanks in advance.
here in planetmath there's a description of it:
http://planetmath.org/encyclopedia/RaabesCriteria.html
i got that the first inequality is correct when mu is smaller than 1.
i got a hint in my test that i should show that {na_(n+1)} is monotonely decreasing, which i did and by another theorem to show c_n=(n-1)a_n-na_(n+1) is convergent which i also did, but i got that
(1-a_(n+1)/a_n)*n=(1-(1-1/n))*n=1>=mu.
where have i gone wrong?
thanks in advance.
Last edited by a moderator: