(1+1/1+3)*(1+1/2*4)*(1+1/3*5)*........*(1+1/98*100)*(1+1/99*101)
来源:百度知道 编辑:UC知道 时间:2024/09/22 02:07:52
规律:1+1/1*3=1*3+1/1*3=4/1*3=2^2/1*3
1+1/3*4=2*4+1/2*4=9/2*4=3^2/2*4
1+1/3*5=3*5+1/3*5=16/3*5=4^2/3*5
...........
根据规律,可猜测:1+1/(2n-1)*(2n+1)=____________(n为整数)
1+1/2n*(2n+2)=__________(n为正整数)
根据规律计算:(1+1/1+3)*(1+1/2*4)*(1+13*5)*(1+1/4*6)*.......*(1+1/18*100)*(1+1/99*101)
1+1/3*4=2*4+1/2*4=9/2*4=3^2/2*4
1+1/3*5=3*5+1/3*5=16/3*5=4^2/3*5
...........
根据规律,可猜测:1+1/(2n-1)*(2n+1)=____________(n为整数)
1+1/2n*(2n+2)=__________(n为正整数)
根据规律计算:(1+1/1+3)*(1+1/2*4)*(1+13*5)*(1+1/4*6)*.......*(1+1/18*100)*(1+1/99*101)
1+1/(2n-1)*(2n+1)=(2n)^2/(2n-1)*(2n+1)(n为整数)
1+1/2n*(2n+2)=(2n+1)^2/2n*(2n+2)(n为正整数)
(1+1/1*3)*(1+1/2*4)*(1+/3*5)*(1+1/4*6)*.......*(1+1/98*100)*(1+1/99*101)=200/101
1+1/(n)*(n+2)=[n*(n+2)+1]/n*(n+2)=(n+1)^2/n*(n+2)=[(n+1)/n]*[(n+1)/(n+2)]
所以
(1+1/1*3)*(1+1/2*4)*(1+1/3*5)*........*(1+1/98*100)*(1+1/99*101)
=(2/1*2/3)*(3/2*3/4)*....(100/99*100/101)
=(2/1*3/2*4/3...99/98*100/99)*(2/3*3/4*...99/100*100/101)
=(100/1)*(2/101)
=200/101
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
(1-1/100)(1-1/99)(1-1/98)......(1-1/3
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100)
1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100)
1+1/2+1+1/3+1+1/4+......+1/100=?
1+1/2+1/3+.....+1/n
1+1/2+1/3+...+1/100
1+1/3+1/6+........+1/55
1-1/2+1/3-.....-1/10