query: Fibonacci proof question $\sum_{i=1}^nF_i = F_{n+2} - 1$
positive_passages.docid: 27217
positive_passages.text: For the Fibonacci sequence prove that $\sum_{i=1}^n F_i= F_{n+2} - 1$
negative_passages.docid: 50655
negative_passages.text: Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$
negative_passages.docid: 141401
negative_passages.text: ${a_n}$ series of Fibonacci numbers. $f(x)=\sum_{0}^{\infty}a_nx^n$, show that in the convergence radius: $f(x)= \frac{1}{1-x-x^2}$
negative_passages.docid: 16177
negative_passages.text: Proof by Induction: $\sum_0^nx^i=(1-x^{n+1})/(1-x)$
negative_passages.docid: 53116
negative_passages.text: How find this sum $f(n)=\sum_{i=1}^{n}\dfrac{\binom{n}{i}}{i}$
negative_passages.docid: 20317
negative_passages.text: Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
negative_passages.docid: 142666
negative_passages.text: Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$
negative_passages.docid: 31245
negative_passages.text: How to prove that Fibonacci number is integer?
negative_passages.docid: 118372
negative_passages.text: Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
negative_passages.docid: 4855
negative_passages.text: How to show that this binomial sum satisfies the Fibonacci relation?
negative_passages.docid: 27968
negative_passages.text: Fibonacci sequence proof
negative_passages.docid: 93984
negative_passages.text: How find this Fibonacci sequence sum $\sum_{k=0}^{\infty}\frac{1}{F_{2^k}}$
negative_passages.docid: 70128
negative_passages.text: Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
negative_passages.docid: 106502
negative_passages.text: Prove by induction that for the Fibonacci numbers $F(n)$ with $n \ge 6$, $F(n) \ge 2^{n/2}$
negative_passages.docid: 91889
negative_passages.text: Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction.
negative_passages.docid: 11612
negative_passages.text: How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
negative_passages.docid: 33082
negative_passages.text: Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.