Almost polynomial equation: least n such that (4^n - 3*3^n - 3*2^n - 1)/(4^n) >= 1/2
Hi everyone, is there any formula (not computing, but solving) to find the least integer n such that :
\(\displaystyle \dfrac {4^{n} - 3\times 3^{n} + 3\times 2^{n} -1}{4^{n}} \geq \dfrac {1}{2} ?\)
I've been facing those kind of inequations since a coupe of days as I'm trying to solve a probability problem : "A teachers has p students, and gives at random one book to one student every day. Each student can get many books. What is the least number of days such that the probability that every student has a book is at least a half".
The first formula is related to the number of 4 students.
Still searching but any piece of advice would be great, thx.
Hi everyone, is there any formula (not computing, but solving) to find the least integer n such that :
\(\displaystyle \dfrac {4^{n} - 3\times 3^{n} + 3\times 2^{n} -1}{4^{n}} \geq \dfrac {1}{2} ?\)
I've been facing those kind of inequations since a coupe of days as I'm trying to solve a probability problem : "A teachers has p students, and gives at random one book to one student every day. Each student can get many books. What is the least number of days such that the probability that every student has a book is at least a half".
The first formula is related to the number of 4 students.
Still searching but any piece of advice would be great, thx.