# proof of raabe criteria.

• March 14th 2006, 03:57 AM
DangerMan
proof of raabe criteria.
does someone know how to prove raabe's criteria for sums convergence?

i tried to prove it with a hint of the book but i got for example if we get from planetmath website, i got that mu is smaller than 1.

because when the sum is convergent:
(1-a_n+1/a_n)*n=1>=mu

i had a hint from my book that i need to prove that {na_n+1} is monotonely decreasing i.e for every n na_n+1>(n-1)a_n and then i only need to prove that c_n=(n-1)a_n-na_n+1 is a convergent sum, which i did but i didn't get the ineality i needed.

any help is appreciated.

Check what this implies for ${\rm limsup}\frac{a_{n+1}}{a_n}$ and use the ratio test.