A) Note that . Furthermore, , which is always positive when . Hence, the minimal value of is , or .
Therefore for all .
Hi, this exercise is giving headaches . I only need help with Part A because I know part B and have an idea of how to solve other exercises similar to part C. Thanks a lot!
The whole exercise says:
"Let for . Define a sequence of real numbers by
for , .
A) Show that if , then .
B) Show that if , then .
C) Conclude that the sequence converges."