The sum of the squares of the first ten natural numbers is, 12 + 22 + ... + 102 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)2 = 552 = 3025 Hence the difference between the sum of the squares of the first ten nat…

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025  385 = 2640. Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.…

The sum of the squares of the first ten natural numbers is, 12 + 22 + ... + 102 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)2 = 552 = 3025 Hence the difference between the sum of the squares of the first ten nat…

简单: e sum of the squares of the first ten natural numbers is, 12 + 22 + ... + 102 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)2 = 552 = 3025 Hence the difference between the sum of the squares of the first ten n…

It is possible to show that the square root of two can be expressed as an infinite continued fraction.  2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213... By expanding this for the first four iterations, we get: 1 + 1/2 = 3/2 = 1.51 + 1/(2 + 1/2) = 7…

In Problem 42 we dealt with triangular problems, in Problem 44 of Project Euler we deal with pentagonal number, I can only wonder if we have to deal with septagonal numbers in Problem 46. Anyway the problem reads Pentagonal numbers are generated by t…

我的做法就是暴力,1+...+n 用前n项和公式就行 1^2+2^2+....+n^2就暴力了 做完后在讨论版发现两个有趣的东西. 一个是 (1+2+3+...+n)^2=(1^3)+(2^3)+(3^3)+...+(n^3) 另一个是 1^2+2^2+....+n^2的公式以及推导. 假设f(n) = an3 + bn2 + cn + d 已知:f(0) = 0; f(1) = 1; f(2) = 5; f(3) = 14 然后带入解方程,得到a,b,c,d,再用归纳法证明其正确性. 证明过程…

Find the sum of all left leaves in a given binary tree. Example: 3 / \ 9 20 / \ 15 7 There are two left leaves in the binary tree, with values 9 and 15 respectively. Return 24. # Definition for a binary tree node. # class TreeNode(object): # def __in…

Given a binary search tree with non-negative values, find the minimum absolute difference between values of any two nodes. Example: Input: 1 \ 3 / 2 Output: 1 Explanation: The minimum absolute difference is 1, which is the difference between 2 and 1…

Calculate the sum of two integers a and b, but you are not allowed to use the operator + and -. Example 1: Input: a = 1, b = 2 Output: 3 Example 2: Input: a = -2, b = 3 Output: 1   class Solution(object): def getSum(self, a, b): """ :type a…