(1+1/1+3)*(1+1/2*4)*(1+1/3*5)*.*(1+1/98*100)*(1+1/99*101)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
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![(1+1/1+3)*(1+1/2*4)*(1+1/3*5)*.*(1+1/98*100)*(1+1/99*101)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](/uploads/image/z/53787-3-7.jpg?t=%281%2B1%2F1%2B3%29%2A%281%2B1%2F2%2A4%29%2A%281%2B1%2F3%2A5%29%2A.%2A%281%2B1%2F98%2A100%29%2A%281%2B1%2F99%2A101%29%E8%A7%84%E5%BE%8B%EF%BC%9A1%2B1%2F1%2A3%3D1%2A3%2B1%2F1%2A3%3D4%2F1%2A3%3D2%5E2%2F1%2A3++++++1%2B1%2F3%2A4%3D2%2A4%2B1%2F2%2A4%3D9%2F2%2A4%3D3%5E2%2F2%2A4++++++1%2B1%2F3%2A5%3D3%2A5%2B1%2F3%2A5%3D16%2F3%2A5%3D4%5E2%2F3%2A5++++++.%E6%A0%B9%E6%8D%AE%E8%A7%84%E5%BE%8B%2C%E5%8F%AF%E7%8C%9C%E6%B5%8B%EF%BC%9A1%2B1%2F%EF%BC%882n-1%EF%BC%89%2A%EF%BC%882n%2B1%EF%BC%89%3D____________%28n%E4%B8%BA%E6%95%B4)
(1+1/1+3)*(1+1/2*4)*(1+1/3*5)*.*(1+1/98*100)*(1+1/99*101)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
(1+1/1+3)*(1+1/2*4)*(1+1/3*5)*.*(1+1/98*100)*(1+1/99*101)
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+1/1+3)*(1+1/2*4)*(1+1/3*5)*.*(1+1/98*100)*(1+1/99*101)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
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