Question

求解一道数学奥数题:1/1*2+1/2*3+1/3*4+1/4*5.1/99*100=

Answer 1

求解一道数学奥数题:1/1*2+1/2*3+1/3*4+1/4*5................1/99*100=

1/1*2+1/2*3+1/3*4+....+1/98*99+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+...+1/98-1/99+1/99-1/100
=1-1/100
=99/100

大家帮忙解一道数学题：1/1*2+1/2*3+1/3*4+.....+1/99*100

套公式！ 1/n(n+1)=1/n-1/(n+1),最后都抵消，的1-1/100

数学题：1/1*2+1/2*3+1/3*4+1/4*5+......1/98*99+1/99*100=?

1/1*2+1/2*3+1/3*4+1/4*5+......1/98*99+1/99*100
=1- 1/2 +1/2 -1/3+……+1/99- 1/100
=1- 1/100
=99/100
在华罗庚六年奥数第一章里有

奥数题1/1×2×3+1/2×3×4+……+1/98×99×100

1/(1×2×3)+1/(2×3×4)+……+1/(98×99×100)
=1/2*[(1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+……+1/(98*99-1/(99*100)]
=1/2*[1/2-1/9900]
=1/4-1/19800
=(4950-1)/19800
=4949/19800

数学奥数题：1/1*2+1/2*3+1/3*4......+1/2011*2012+1/2012*2013

1/1*2+1/2*3+1/3*4......+1/2011*2012+1/2012*2013
=1-1/2+1/2-1/3+1/3-1/4+...+1/2011-1/2012+1/2012-1/2013
=1-1/2013
=2012/2013

奥数题 1/2+1/3+1/4+1/6+1/12+1/48+1/56

1/2(24/48)+1/3(16/48)+1/4(12/48)+1/6(8/48)+1/12(4/48)+1/48+1/56
=72/48(3/2=84/56)+1/56=85/56

奥数题6年级1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...1/39*40

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...1/39*40
=1-1/2+1/2-1/3+...+1/39-1/40
=1-1/40
=39/40

数学 1/1×2+1/2×3+1/3×4+...+1/99×100

1/1*2+1/2*3+1/3*4+...+1/99*100
=1-1/2+2/1-1/3+1/3-1/4+...+1/99-1/100
=1-1/100
=99/100

求助数学题 1/1*2+1/2*3+1/3*4+…+1/99*100=?

这是一道典型的问题，用裂项法很简单
1/1*2=1/2=1-1/2
1/2*3=1/6=1/2-1/3
1/3*4=1/12=1/3-1/4
……
1/99*100=1/99-1/100
将上述等式相加：
其中-1/2与1/2、-1/3与1/3……-1/99与1/99相互抵消，最后只剩下1-1/100
所以，本题答案为99/100

数学：1/1*2*3+1/2*3*4+1/3*4*5+......1/99*100*101

原式=1/2*[1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+...+1/(99*100)-1/(100*101)]
=1/2*[1/(1*2)-1/(100*101)]
=1/2*[1/2-1/10100]
=1/2*(5049/10100)
=5049/20200