What must be the simplest proof of the sum of first $n$ natural numbers?
2675
Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$
65763
Number of ways to write n as a sum of k nonnegative integers
87257
How to prove this sequent using natural deduction?
107433
Prove the sum to n terms of the series
58264
How to derive the formula for the sum of the first $n$ perfect squares?
69875
Prove the commutativity property of addition of natural numbers by induction
26087
Find all natural numbers $n > 1$ and $m > 1$ such that $1!3!5!\cdots(2n - 1)! = m!$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
94620
Which number was removed from the first $n$ naturals?
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
111298
Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
15164
Proof of $\sum^{2N}_{n=1} \frac{(-1)^{n-1}}{n} = \sum^{N}_{n=1} \frac{1}{N+n}$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
83037
Applying Zorn's Lemma to natural numbers
21612
How to prove this form of $n$?
92106
Prove that $n$ is a sum of two squares?