n+n+collocation

梁月非47231+1/2+1/3.1/n>ln(n+1)的证法 -
连于田13882081762 ______[答案] 1>ln2 1/2>ln3/2 1/3>ln4/3 …… 1/n>ln((n+1)/n) 所以1+1/2+1/3.1/n>ln2+ln3/2+ln4/3+……+ln((n+1)/n)=ln(2*3/2*4/3*……*(n+1)/n)=ln(n+1)

梁月非47231*2+2*3+'''+n(n+1)=? -
连于田13882081762 ______[答案] 令s(n)=1*2+2*3+3*4+…+n*(n+1) 则,s(n+1)=1*2+2*3+3*4+…+n*(n+1)+(n+1)*(n+2) s(n+1)-s(n)=(n+1)*(n+2)=n^2+3n+2 依次带入: n=1时,s(2)-s(1)=1^2+3*1+2 n=2时,s(3)-s(2)=2^2+3*2+2 …… 然后叠加: 得到s(n)-s(1)=【1^2+2^2+……n^2】+3*...

梁月非4723求和n*(1*2)+(n - 1)*(2*3)+(n - 2)*(3*4)+...+2*(n - 1)*n+n*(n+1) -
连于田13882081762 ______[答案] =n*(1*2+2*3+3*4+...+n*(n+1)) - (0*1*2-1*2*3-2*3*4-...-(n-1)n(n+1)) =n*n*(n+1)*(n+2)/3-(n-1)n(n+1)(n+2)/4 =n(n+1)(n+2)(n+3)/24.

梁月非47231^2+2^2+3^2+4^2+...+n^2怎么推导? -
连于田13882081762 ______[答案] 1^2+2^2+3^2+4^2+5^2………………+n^2=n(n+1)(2n+1)/6 利用立方差公式 n^3-(n-1)^3=1*[n^2+(n-1)^2+n(n-1)] =n^2+(n-1)^2+n^2-n =2*n^2+(n-1)^2-n 2^3-1^3=2*2^2+1^2-2 3^3-2^3=2*3^2+2^2-3 4^3-3^3=2*4^2+3^2-4 . n^3-(n-1)^3=2*n^2+(n-1)^2-n 各...

梁月非4723如果;m+m+m+n+n=54 m+m+n+n=46,那么m=( ),n=( ). -
连于田13882081762 ______[答案] m+m+m+n+n=54 m+(m+m+n+n)=54 m+46=54 m=8, n=15.

梁月非47231x2+2x3+3x4+...+n(n+1)=? -
连于田13882081762 ______[答案] 1x2+2x3+3x4+...+n(n+1)=1^2+1+2^2+2+3^2+3+...+n^2+n=1+2+...+n+(1^2+2^2+...+n^2)=(1+n)n/2+n(n+1)(2n+1)/6=n(n+1)/2*(1+(2n+1)/3)=n(n+1)(2n+5)/6---看通项,再分解,利用公式!

梁月非4723如果实数m≠n,且8m+n8n+m=m+1n+1,则m+n=( ) -
连于田13882081762 ______[选项] A. 7 B. 8 C. 9 D. 10

梁月非4723python编写1+(1+3)+(1+3+5)+……(1+3+5+……+n)和的程序 -
连于田13882081762 ______ #!/usr/bin/python3 def fun(n): if n < 0 or n%2 == 0: raise Exception('参数必须是正奇数') sum = 0 for j in range(n//2+1): for i in range(1,(j+1)*2,2): sum += i return sum print(fun(7))原创代码,fun函数参数可换成其他正奇数,参数检测有错误抛异常,不懂之处追问.

梁月非4723lim1/n+1/(n+1)+.1/2n=?n趋近没穷大 -
连于田13882081762 ______[答案] lim1/n+1/(n+1)+.1/2n=lim{(1/n)*(1/(1+0/n)+1/(1+1/n)+1/(1+2/n)+……+1/(1+n/n))}=函数1/(1+x)在区间[0,1]上的定积分=ln(1+1)-ln(1+0)=ln2

梁月非4723数学归纳法证明:1+1/2+1/3+...+1/n>In(n+1)需要第二步的详细过程. -
连于田13882081762 ______[答案] 关键步骤:证明ln(n+1)-In(n)