Infinite Finite Difference

Calculus Level 4

Let \( a_n \) be a real sequence with positive terms such that \( \displaystyle \lim_{n\to \infty} a_n = 0 \).

If the sequence \( c_n = a_n - a_{n+1} \) is nonincreasing, what is the strongest statement we can make about the limit \( \displaystyle \lim_{n\to \infty} n c_n \) (that is true for any choice of \( a_n \))?

×

Problem Loading...

Note Loading...

Set Loading...