Prove $99^{100}>100^{99}$ using binomial theorem
91690
Which of the numbers $99^{100}$ and $100^{99}$ is the larger one?
126214
Multiplying Binomial Terms
96673
Prove central binomial coefficient upper bound
73050
Explanation of the binomial theorem and the associated Big O notation
155769
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ using the binomial theorem for $n\geq1$
27560
How many zeroes are in 100!
130223
Proving a special case of the binomial theorem: $\sum^{k}_{m=0}\binom{k}{m} = 2^k$
88268
show $\frac{1}{15}< \frac{1}{2}\times\frac{3}{4}\times\cdots\times\frac{99}{100}<\frac{1}{10}$ is true
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
4327
proving $\left(1+\frac 1n\right)^{n} = 1 + \sum_{k=1}^n \{\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn)\}$ using the binomial theorem
118036
Proving at least 99 pairwise sums of the reals are non-negative
119759
Help ending a proof using binomial theorem: $\sum_{k=0}^n {n \choose k}\cdot\frac{(-1)^k}{k+1} = \frac{1}{n+1}$
36514
Show that $45<x_{1000}<45.1$
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$
12250
How to find the prime factorization of $100!$.
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$