query: Finding numbers from quotient of sums with roots.
positive_passages.docid: 46401
positive_passages.text: Value of $\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\cdots+\sqrt{10+\sqrt{99}} }{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\cdots+\sqrt{10-\sqrt{99}}}$
negative_passages.docid: 31184
negative_passages.text: Sums of powers below a prime
negative_passages.docid: 28489
negative_passages.text: Estimating partial sums $\sum_{n = 1}^m \frac{1}{\sqrt{n}}$
negative_passages.docid: 7891
negative_passages.text: Sum of nth roots of unity
negative_passages.docid: 129801
negative_passages.text: Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
negative_passages.docid: 110444
negative_passages.text: Finding out the number of divisors
negative_passages.docid: 26446
negative_passages.text: Find the sum : $\displaystyle\sum_{i=0}^n \frac{2^i}{1+x^{2^{i}}}$
negative_passages.docid: 11359
negative_passages.text: Determine the Set of a Sum of Numbers
negative_passages.docid: 112253
negative_passages.text: How to find sums like $\sum_{k=0}^{39} \binom{200}{5k}$
negative_passages.docid: 72402
negative_passages.text: Summation of natural number set with power of $m$
negative_passages.docid: 62463
negative_passages.text: A pencil approach to find $\sum \limits_{i=1}^{69} \sqrt{\left( 1+\frac{1}{i^2}+\frac{1}{(i+1)^2}\right)}$
negative_passages.docid: 108035
negative_passages.text: solving diophantine equations using congruences
negative_passages.docid: 14884
negative_passages.text: Compute a sum with partial fraction decomposition and generating functions
negative_passages.docid: 103304
negative_passages.text: Finding the number of solutions to a diophantine equation
negative_passages.docid: 31977
negative_passages.text: How to prove sum of powers property of roots of unity?
negative_passages.docid: 18903
negative_passages.text: Finding solutions to equation of the form $1+x+x^{2} + \cdots + x^{m} = y^{n}$
negative_passages.docid: 74058
negative_passages.text: Sums and products of algebraic numbers