Matematické Fórum

Skrytý text:
We use difference calculus in an elementary level and a few estimations.

For a real sequence we define a difference operator as follows:



Then for two real sequences and we have



If both sequences are the same we get the special case of the previous identity



The given sequence satisfies the following identities:



On the other hand we can express the sum in the left hand side also using the identity , thus



Now we estimate the term from bellow and from above.

1. It is obvious that

2. On the other hand we use the fact that and the identity twice and we deduce that



So we have shown that



Finally we apply the squezze theorem: