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include "stdio.h"#include "math.h"int main(int argc,char *argv[]){int n,i;double s;printf("Input n(int n>0)...\nn=");if(scanf("%d",&n)!=1 || n<1){printf("Input error, exit...\n");return 0;}for(s=0;n;n--)for(i=1;i<=n;s+=sqrt(i++));printf(...
计算并输入s=1+(1+√2)+(1+√2+√3)+...+(1+√2+√3+...+√n)include <MATH.H> int main(){ int n;printf("Input n(n>0):\n");scanf("%d", &n);int i=0, j=0;double s=0.0, ss=0.0;for(i=1; i<=n; i++){ ss=0.0;for(j=1;j<=i;j++){ ss+=sqrt(j);} s+=ss;} printf("s=%lf\n", s);return 0;} ...
计算并输入s=1+(1+√2)+(1+√2+√3)+...+(1+√2+√3+...+√n)int main(void){ double sum = 0.0, sumSub = 0.0;int i = 0;int n = 0;printf("Input N: ");scanf("%d", &n);for(i = 1; i <= n; i++){ sumSub = sumSub + sqrt(i); //1+√2+√3+...+√n sum = sum + sumSub; //1+(1+√2)+(1+√2+√3...
...数学题√(1+√(2+√(3+√(4...+√(99+√(100)))的和大约是1.757932757 计算用Excel,A1..A100=1..100,B100=SQRT(A100),B1..B99=SQRT(A1..A99+B2..B100),结果在B1
sqrt(1+sqrt(2+sqrt(3+sqrt(4+...sqrt(n))),当n趋于无穷时,它是否收敛...是收敛的。这里我提示你一个思路 令:x_n=sqrt(1+sqrt(2+sqrt(3+sqrt(4+...sqrt(n)))构造函数:f_n (x)=sqrt(1+sqrt(2+sqrt(3+sqrt(4+...sqrt(n+x)))则:你可以估计x_(n+1)=f_n (sqrt(n+1))那么你可以估计(利用拉格朗日中值定理就可以了)x_(n+1)-x_n <1/...
正整数开根号写成连分数是否都是循环的?譬如sqrt(3)=[1;1,2,1,2,1...非平方正整数开平方根(二次根号),写成连分数是否都是循环的?答:是的。证:设sqrt(n)=y=m+x, 其中m=int(sqrt(n)),这里int表示取整数部分,有时也用[]或┌ ┐ 表示。于是 n=yy,xx+2mx=yy-mm=n-mm,即x(x+2m)=n-mm 于是x+2m=(n-mm)/x 于是1/x=(2m+x)/(n-mm)=......
1+1/√2+1/√3+1/√4+…+1/√2025=include<stdio.h> include<math.h> int main(){ double sum=0;int i;for(i=1; i<2026; i++){ sum=sum+1.0/sqrt(i);} printf("%lf\n",sum);return 0;}
方程x=sqrt(x+1)+sqrt(x+2)+sqrt(x+3)+sqrt(x+4)的解是代数数吗?其中...方程可去掉根号,化为多项式方程,因此X是代数数:令x+2=t^2 ,x=t^2-2 t^2-2=√(t^2-1)+t+√(t^2+1)+√(t^2+2)t^2-t-2-√(t^2+2)=√(t^2-1)+√(t^2+1),两边平方得:a^2-2a√(t^2+2)+(t^2+2)=2t^2+2√(t^4-1), a=t^2-t-2 b=a√(t^2...
u1=√a ,u2=√(a+√a),un=√(a+un-1),证明当n->∞,limun存在下面就用数学归纳法证明un<(1+sqrt(1+4a))/2 u1=√a<(1+sqrt(1+4a))/2 假设n=k时成立,即uk<(1+sqrt(1+4a))/2 则uk+1=√(a+uk)<√(a+(1+sqrt(1+4a))/2)<=1+sqrt(1+4a))/2 所以n=k+1也成立 所以un<(1+sqrt(1+4a))/2 下证单调递增:因为un<(1+sqrt(1+4a)...
已知函数f(x)=√3sinxcosx-1/2cos∧2x+1/2sin∧2x-1- 1 = sin(2x - pi/6) - 1 (1) 最大值0,最小sin(-pi/6) - 1 = -1.5 (2) f(C) = 0, 2C-pi/6 = pi/2, C = pi/3 sinA/1 = sinB/2 sinB = 2sinA a/sinA = c/sinC = 2 a = 2sinA b = 2sinB = 4sinA b = 2a a = 1, b = 2, c = sqrt(3)