query: What is the unit digit of $ 1^1+2^2+3^3+...+2018^{2018} $?
positive_passages.docid: 18093
positive_passages.text: Find $x$ such that $\sum_{k=1}^{2014} k^k \equiv x \pmod {10}$
negative_passages.docid: 19449
negative_passages.text: What is $48\div2(9+3)$?
negative_passages.docid: 153796
negative_passages.text: How to define fractional factorials, like 3.6!?
negative_passages.docid: 109640
negative_passages.text: How do i find $(1+i)^{100}?$
negative_passages.docid: 79170
negative_passages.text: $1 + \frac{1}{1+2}+ \frac{1}{1+2+3}+ ... + \frac{1}{1+2+3+...+n} = ?$
negative_passages.docid: 15725
negative_passages.text: $2017$ as the sum of two squares
negative_passages.docid: 25426
negative_passages.text: A sum of series problem: $\frac{3}{1!+2!+3!} + \frac{4}{2!+3!+4!} + \cdots + \frac{2008}{2006!+2007!+2008!}$
negative_passages.docid: 117843
negative_passages.text: Finding the sum of series $\sum_{n=0}^∞ \frac{2^n + 3^n}{6^n}$
negative_passages.docid: 49116
negative_passages.text: Finding the last digit of $103^{103^{103^{103^{103}}}}$
negative_passages.docid: 115170
negative_passages.text: What is the formula for this numerical series?
negative_passages.docid: 28661
negative_passages.text: What will be the one's digit of the remainder in: $\left|5555^{2222} + 2222^{5555}\right|\div 7=?$
negative_passages.docid: 72406
negative_passages.text: Last two digits of $2^{1000}$ via Chinese Remainder Theorem?
negative_passages.docid: 49194
negative_passages.text: Given a double, need to find how many digits in total
negative_passages.docid: 72437
negative_passages.text: Sum of the digits of a perfect square
negative_passages.docid: 71824
negative_passages.text: Finding the sum of the series $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \ldots$
negative_passages.docid: 27249
negative_passages.text: How many digits does $2^{1000}$ contain?
negative_passages.docid: 103493
negative_passages.text: Find the $1000$th digit after the decimal point of $\sqrt{n},$ where $n=\underbrace{11\dots1}_{1998 \text{ 1's}}$