Show that $n$ can be written in the form $n=c_{0}+c_{1}d+...+c_{k}d^{k}$
129163
Showing that every positive integer can be represented in this form
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
104274
Express $C$ interms of the sets $A_n$
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
113331
Number of ways a natural number can be written as sum of smaller natural number
75317
Show that $(s_n)$ is a Cauchy sequence
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
110441
Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$
102042
If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$
111298
Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
20467
Show that $(y_n)\in l^q$
92704
Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
103347
combinatorial proof of summation
89175
Proof of $(a+b)^{n+1}$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$