query: Big-Theta sum rule proof
positive_passages.docid: 24951
positive_passages.text: Suppose $f_1 \in \Theta(g_1) \land f_2 \in \Theta(g_2)$. Prove $f_1 + f_2 \in \Theta(\max\{g_1, g_2\})$.
negative_passages.docid: 120976
negative_passages.text: Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
negative_passages.docid: 48503
negative_passages.text: Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
negative_passages.docid: 113080
negative_passages.text: Prove $\tan\big(\frac{\pi}{2} -\theta \big) = \cot \theta$
negative_passages.docid: 112080
negative_passages.text: Proving the Product Rule for exponents with the same base
negative_passages.docid: 101899
negative_passages.text: Proof By Induction of a Sum
negative_passages.docid: 44621
negative_passages.text: Simple binomial theorem proof: $\sum_{j=0}^{k} \binom{a+j}j = \binom{a+k+1}k$
negative_passages.docid: 44391
negative_passages.text: How can I prove $n - 2\sqrt{n} = \Theta(n)$
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof
negative_passages.docid: 53899
negative_passages.text: Proof of the Sherman-Morrison Formula
negative_passages.docid: 12484
negative_passages.text: Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
negative_passages.docid: 45460
negative_passages.text: Proof verification of a number theory problem involving sequences.
negative_passages.docid: 151935
negative_passages.text: Proving the predicate $\forall n \in \mathbb{N} , n \geq 2$ using the Pigeonhole principle
negative_passages.docid: 86348
negative_passages.text: Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$
negative_passages.docid: 133905
negative_passages.text: Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
negative_passages.docid: 56828
negative_passages.text: A combinatorial proof that the alternating sum of binomial coefficients is zero
negative_passages.docid: 3632
negative_passages.text: Basic number theory proofs