Binomial Recurrence for $f(n) = \sum \binom{n-i}{i}$
48610
Fibonacci Numbers Proof: $ f_n = \binom n0 + \binom{n-1}1 +\dots+ \binom{n-k}k$
4855
How to show that this binomial sum satisfies the Fibonacci relation?
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
79266
Proving a sequence defined by a recurrence relation converges
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
137012
Mathematical Induction for Recurrence Relation
17604
What is a good asymptotic for $f_n = f_{n-1}+\ln(f_{n-1})$?
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
81371
Solving recurrence $T(n) = T(\lceil n/2 \rceil) + T(\lfloor n/2 \rfloor) + \Theta(n)$
1167
How to prove that $\sum_{k=0}^{n}(-1)^k \binom {n}{k}=0 $
1711
Quadratic Recurrence : $f(n) = f(n-1) + f(n-2) + f(n-1) f(n-2)$ Solution? How?
92235
Explicit formula for Bernoulli numbers by using only the recurrence relation
117761
When is $\binom{n}{k}$ divisible by $n$?
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
17492
Recurrence telescoping $T(n) = T(n-1) + 1/n$ and $T(n) = T(n-1) + \log n$
155769
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ using the binomial theorem for $n\geq1$