In the harmonic series 1+1/2+1/3+1/4+... we omit expressions which contain digit 9 in denominator (so we omit e.g. 1/9, 1/19, 1/94, 1/893, 1/6743090 etc.). Proof that such series is convergent.
Have You got any idea how to solve this problem?
Thanks a lot for help
Find limit n-->infinity of sequence a_n:
a_n = (1^k+2^k+...+n^k)/(n^(k+1)), where k is parameter.
IThanks from advance for any help.
I tried to compute this limit using Stolz Theorem, but I don't know if I can do it in this way.
Sequences a_n and b_n are defined in the follwing way:
a_1=x;
b_1=y;
where 0<x<y
and:
a_(n+1) = (a_n+b_n)/2
b_(n+1) = sqrt(a_(n+1)+b_n)
Proof, that both sequences are convergent to the same limit and find this limit.
Thanks a lot for any help.