作业帮1.观察下列各式： 1\2=1\1*2=1\1-1\2 , 1\6=1\2*3=1\2-1\3 , 1\12=1\3*4=1\3-1\4 &
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1.观察下列各式： 1\2=1\1*2=1\1-1\2 , 1\6=1\2*3=1\2-1\3 , 1\12=1\3*4=1\3-1\4 &
1.观察下列各式： 1\2=1\1*2=1\1-1\2 , 1\6=1\2*3=1\2-1\3 , 1\12=1\3*4=1\3-1\4 ...
(1):通过观察,你得到什么结论?用含有N(N为正整数)的等式表示:
(2):利用你得到的结论,计算1\X(X+1)+1\(X+1)(X+2)+.+1\(X+4)(X+5)
2.X\(X-3)-1\X=1
3.1\(X+1)+2\(X-1)=4\(X^2-1)
1.观察下列各式： 1\2=1\1*2=1\1-1\2 , 1\6=1\2*3=1\2-1\3 , 1\12=1\3*4=1\3-1\4 &
(1):通过观察,你得到什么结论?用含有N(N为正整数)的等式表示:
1/n(n+1)=1/n-1/(n+1)
(2):利用你得到的结论,计算1\X(X+1)+1\(X+1)(X+2)+.+1\(X+4)(X+5)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+4)-1/(x+5)
=1/x-1/(x+5)
=5/[x(x+5)]
2.X\(X-3)-1\X=1
x/(x-3)=1/x+1=(1+x)/x
x^2=(x-3)(1+x)
x^2=x^2-2x-3
x=-3/2
3.1\(X+1)+2\(X-1)=4\(X^2-1)
1/(x+1)+2/(x-1)=4/(x-1)(x+1)
1/(x+1)+2/(x-1)=2[1/(x-1)-1/(x+1)]
1/(x+1)=-2/(x+1)
3/(x+1)=0
方程无解.
1.
1) 1\[(N+1)*N]=1\N*(N+1)=1\N-1\(N+1)
2) 1\X(X+1)+1\(X+1)(X+2)+......+1\(X+4)(X+5)
=1\X-1\(X+1)+1\(X+1)-1\(X+2).....+1\(X+4)-1/(X+5)
=1\X-1\(X+5)
...
全部展开
1.
1) 1\[(N+1)*N]=1\N*(N+1)=1\N-1\(N+1)
2) 1\X(X+1)+1\(X+1)(X+2)+......+1\(X+4)(X+5)
=1\X-1\(X+1)+1\(X+1)-1\(X+2).....+1\(X+4)-1/(X+5)
=1\X-1\(X+5)
=(X+5-X)\X*(X+5)
=0
2.X\(X-3)-1\X=1
x/(x-3)=1/x+1=(1+x)/x
x^2=(x-3)(1+x)
x^2=x^2-2x-3
x=-3/2
3.1\(X+1)+2\(X-1)=4\(X^2-1)
X-1+2X+2=4
3X=3
X=1
收起
1)、1/N(N+1) = 1/N - 1/(N+1)
2)、1/X - 1/(X+5)
最后两行是要干嘛？证明的？？
1.(1) 1/n*(n+1)=1/n - 1/(n+1) (n为正整数)
(2)原式=1/x - 1/(x+1) + 1/(x+1) - 1/(x+2) + ...... +1/(x+4) - 1/(x+5)
=1/x - 1/(x+5)
请问后俩题要问什么？
1，1/n-1/(n+1)=1/[n*(n+1)]
2,原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)……1/(x+4)-1/(x+5)=1/x-1/(x+5)=
-5/(x^2-5x)
2,x/(x-3)-1/x=1
化简整理得 （2x+3)/(x^2-3x)=0
因为分母不为零，x=-3/2
3,原式化简得，（3x+1)/(x^2-1)=4/(x^2-1)
整理得（3x-3)/(x^2-1)=0
解得x无解
1 ①1/n=1/n*(n+1)=1/n-1/(n+1)
②原式=1/x-1/(x+1)+1/(x+1)-1/(x+2）+…-1/（x+5）=1/x-1/(X+5)
2 X=1.5
3 X=1
1/n(n+1)=1/n-1/(n+1)
1\X(X+1)+1\(X+1)(X+2)+......+1\(X+4)(X+5)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+4)-1/(x+5)
=1/x-1/(x+5)
=5/[x(x+5)]
2.X\(X-3)-1\X=1
x/(x-3)=1/x+1=(1+x)/x
全部展开
1/n(n+1)=1/n-1/(n+1)
1\X(X+1)+1\(X+1)(X+2)+......+1\(X+4)(X+5)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+4)-1/(x+5)
=1/x-1/(x+5)
=5/[x(x+5)]
2.X\(X-3)-1\X=1
x/(x-3)=1/x+1=(1+x)/x
x^2=(x-3)(1+x)
x^2=x^2-2x-3
x=-3/2
3.1\(X+1)+2\(X-1)=4\(X^2-1)
1/(x+1)+2/(x-1)=4/(x-1)(x+1)
1/(x+1)+2/(x-1)=2[1/(x-1)-1/(x+1)]
1/(x+1)=-2/(x+1)
3/(x+1)=0
收起