$[问题]证明\pi是无理数$ math latex中文字为解答,斜体文字为注释 [解答]首先还是老套路,设\pi=\frac{a}{b} 令f(x)=\frac{x^n(a-bx)^n}{n!}① 之所以要写成这种分母为n!的形式,是为了方便后面用麦克劳林展开比较系数 所以f(x)=\frac{b^nx^n(\pi-x)^n}{n!}② 由②易得f(x)……

思考题 with song 75 There have been 73 heroes failing to rescue the princess, and the 74-th was killed by the princess. As the 75-th knight, you decided to become stronger so that you would survive the princess's attack. You are given a directed g……

Readers, we present, the Ultimate Reading Comprehension Challenge! If you don't know what Reading Comprehension is, it's about you are given a passage, you read it and answer the question. Sounds neat, but this time we will something crazy! We'll g……

思考题 with anime Unlimited Fafnir After watching the famous anime Unlimited Fafnir, XGN got excited. So he decided to recreate the scene of fighting the Basilisk. This time, Yuu is going to do it himself. Let's suppose the world is a 2D plane. The……

思考题so late? Dazzit Again This is an easy version of OBCYSIO 28) You are given an integer sequence A of length N and another sequence B of length M. Then imagine a game: First, you choose exactly M different elements and arrange them, let's call ……

Contest Link If you haven't read the problems or tried to solve it yourself, don't read this. A - Clock Difficulty: d2b Hint The hour hand of the clock moves 0.5 degree per minute, the minute hand of the clock moves 6 degree per minute. Then it tur……

这是一个神必的不等式技巧,睡觉时候想的,我也不知道对不对,用就完事儿了 :/ 0.1 如图,这是一个严格上凸函数y=f(x) 它的上面有两点(x_0,y_0),(x_1,y_1) 先做出这两点的2条切线,再将这两点连起来 易观察得斜率由大到小分别是左边切线,中间连线,右边切线 证明亦不难: 由……

This is an easy algebra problem. I believe clever jgh must can solve it in 1min! We know that x-\frac{y}{z}-\frac{z}{y}=y-\frac{x}{z}-\frac{z}{x}=z-\frac{x}{y}-\frac{y}{x}=a and x {\neq}y{\neq}z (1) What is the value of x+y+z ? (2) What is the valu……

思考题 for 2020 DuiLian 二十年飞花不尽 一几度落月无穷 九州同乐 Of twenty years, the flower never withers In one eternity, the moon forever remains Enjoy it together It's 2020 soon. It's time for the biggest holiday - The Yuandan and the Chinese Ne……

思考题 about cheating Lottery Cheating Let's have some lottery! In this lottery system, a number string S and an array of integers A is predetermined. It is known that |A|=|S| and let's define A_0=0. Each user chooses a number string T(|T|=|S|). Th……