Question

急、急！一道简便方法计算题！50悬赏分！

1/(2*4*6)+1/(4*6*8)+……+1/（96*98*100）
要最详细的！！！

Answer 1

1/(2*4*6)+1/(4*6*8)+……+1/（96*98*100）=
1/4[1/(2*4)-1/(4*6)+1/(4*6)-1/(6*8)……+
......1/96*98-1/98*100 ](中括号内第二,三项互相抵消,四,五项互相抵消....只剩第一项和最后一项)
=1/4[1/(2*4)-1/(98*100]
=1/4×[(49×25-1)/(8*49*25)]
=1/4×(1224/9800)
306/9800
=153/4900

Answer 2

1/(2K*(2K+2)*(2K+4))=1/16*(1/k+1/(K+2)-2/(K+1))
所以:
S=1/16*(1-1/2+1/100-1/98)=
中间项自己消一下,写出几列,就知道什么象能全消,什么项不能全消,就第一项和最后一项中有东西不能消掉,其他全消掉了

Answer 3

∵1/(2×4)-1/(4×6)=4/(2×4×6),1/(4×6)-1/(6×8)=4/(4×6×8),...
1/(96×98)-1/(98×100)=4/(96×98×100)；
∴1/(2×4×6)+1/(4×6×8)+...+1/(96×98×100)
=1/4[4/(2×4×6)+4/(4×6×8)+...+4/(96×98×100)]
=1/4{[1/(2×4)-1/(4×6)]+[1/(4×6)-1/(6×8)]+...+[1/(96×98)-1/(98×100)]}
=1/4{1/(2×4)-1/(98×100)}
=1/4×1224/9800
=153/4900.

Answer 4

原式=1/8*(1/(1*2*3)+1/(2*3*4)+...+1/(48*49*50))
因为,1/(N-1)-2/N+1/(N+1)=2/((N-1)*N*(N+1))
所以,上式=1/16*(1-2/2+1/3+1/2-2/3+1/4+1/3-2/4+1/5+...+1/48-2/49+1/50)
=1/16*(1-1/2-1/49+1/50)
=153/4900

Answer 5

=1/4{[1/(2×4)-1/(4×6)]+[1/(4×6)-1/(6×8)]+...+[1/(96×98)-1/(98×100)]}
=1/4{1/(2×4)-1/(98×100)}
=153/4900.