Estimate of a combination number by another
Task number: 3854
Estimate \(\binom{2m+1}{m}\) from both sides by a function of \(\binom{2m}{m}\).
Solution
From Pascal’s triangle we have \(\binom{2m+1}{m}=\binom{2m}{m}+\binom{2m}{m+1}\), while \(\binom{2m}{m}>\binom{2m}{m+1}>0\).
Then straightforwardly.
Answer
The desired estimate could be e.g. \(\binom{2m}{m}<\binom{2m+1}{m}<2\binom{2m}{m}\).
