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15 Answered Questions

[SOLVED] Proof of the Hockey-Stick Identity: $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$

31 Answered Questions

[SOLVED] Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$

9 Answered Questions

[SOLVED] How to compute the formula $\sum \limits_{r=1}^d r \cdot 2^r$?

5 Answered Questions

[SOLVED] Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?

6 Answered Questions

[SOLVED] Questions on "All Horse are the Same Color" Proof by Complete Induction

3 Answered Questions

[SOLVED] Mod of numbers with large exponents

8 Answered Questions

[SOLVED] Fibonacci addition law $F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$

6 Answered Questions

[SOLVED] Using proof by contradiction vs proof of the contrapositive

6 Answered Questions

[SOLVED] Why is mathematical induction a valid proof technique?

6 Answered Questions

[SOLVED] Number of occurrences of k consecutive 1's in a binary string of length n (containing only 1's and 0's)

5 Answered Questions

[SOLVED] Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$

4 Answered Questions

[SOLVED] Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $

2 Answered Questions

[SOLVED] Show that $n$ lines separate the plane into $\frac{(n^2+n+2)}{2}$ regions

2 Answered Questions

[SOLVED] Counting number of moves on a grid

5 Answered Questions

[SOLVED] How many distinct functions can be defined from set A to B?

5 Answered Questions

[SOLVED] Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$

5 Answered Questions

[SOLVED] $A \oplus B = A \oplus C$ imply $B = C$?

6 Answered Questions

[SOLVED] General formula for the 1; 5; 19; 65; 211 sequence

4 Answered Questions

[SOLVED] Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$

3 Answered Questions

[SOLVED] How to get the correct angle of the ellipse after approximation

5 Answered Questions

[SOLVED] Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction

5 Answered Questions

[SOLVED] Show that if $g \circ f$ is injective, then so is $f$.

4 Answered Questions

[SOLVED] Prove by Mathematical Induction: $1(1!) + 2(2!) + \cdot \cdot \cdot +n(n!) = (n+1)!-1$

3 Answered Questions

[SOLVED] Prove $f(S \cup T) = f(S) \cup f(T)$

2 Answered Questions

[SOLVED] Coupon Collector Problem with Batched Selections

4 Answered Questions

[SOLVED] Sum of cubes proof

2 Answered Questions

[SOLVED] What exactly is the difference between weak and strong induction?

2 Answered Questions

[SOLVED] Choosing numbers without consecutive numbers.

2 Answered Questions

[SOLVED] Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.

8 Answered Questions

[SOLVED] What is $\gcd(0,0)$?

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