FuzzyPixelz

### Questions (24)

 5 Considering sets in proofs 5 Proving that a complex number is nonreal. 4 Combinatorial proof for $\sum_{k=0}^p (-1)^k {n \choose k} = (-1)^p {n-1 \choose p}$ [duplicate] 3 How to solve the equation $3x-4\lfloor x\rfloor=0$ for $x\in\mathbb{R}$? 2 Limit of a sum using complex analysis.

### Reputation (387)

 +5 Proof of $\sum_{k=n-1}^{n+p-1} {k \choose p}={n+p \choose p}$ using the equation $x_1 + x_2 + \dots + x_n = p$ +5 Combinatorial proof for $\sum_{k=0}^p {p+q\choose k} {p+q-k\choose p-k}=2^p {p+q \choose p}$ +20 Combinatorial proof for $\sum_{k=0}^p (-1)^k {n \choose k} = (-1)^p {n-1 \choose p}$ -2 If a number irrational, can it be rational in some rational-based number system?

### Answers (6)

 4 What is the value of $a/b/c$? 2 If a number irrational, can it be rational in some rational-based number system? 2 Find $x$ such that $4\sqrt x+\sqrt 2=3\sqrt 2$ 1 Show that $(1+e^{ix})(1+e^{-ix}) = 2 + 2\cos x$ 0 How to tell if a function generates a positive value or a negative value?

### Tags (39)

 4 divisibility 1 complex-numbers × 7 4 definition 1 trigonometry × 2 2 number-systems 0 summation × 5 2 radicals 0 proof-writing × 4 2 algebra-precalculus 0 real-analysis × 3

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