分式数列求解:1/(100*101)+1/(101*102)+1/(102*103)+.+1/(149*150);分子为1;急._百度作业帮
分式数列求解:1/(100*101)+1/(101*102)+1/(102*103)+.+1/(149*150);分子为1;急.
分式数列求解:1/(100*101)+1/(101*102)+1/(102*103)+.+1/(149*150);分子为1;急.
1/(n(n+1))=(n+1 -n)/(n(n+1))=1/n-1/(n+1) ∴ 1/(100*101)=1/100-1/101 1/(101*102)=1/101-1/102 1/(102*103)=1/102-1/103 .1/(149*150)=1/149-1/150 以上式子左右分别相加得:1/(100*101)+1/(101*102)+1/(102*103)+.+1/(149*150)=1/100-1/150 =1/300 总和为1/300150-149+148-147+...+104+104-103+102-101用奥数怎么写_百度作业帮
150-149+148-147+...+104+104-103+102-101用奥数怎么写
150-149+148-147+...+104+104-103+102-101用奥数怎么写
(150-149)+(148-147)+...+(104-103)+(102-101)=1+1+1+1…+1=1×25=25急,问1/100*101+1/101*102+1/102*103+.1/149*150怎么解?拜托各位大神_百度作业帮
急,问1/100*101+1/101*102+1/102*103+.1/149*150怎么解?拜托各位大神
急,问1/100*101+1/101*102+1/102*103+.1/149*150怎么解?拜托各位大神
1/100*101+1/101*102+1/102*103+.1/149*150,将式子划减,方法是1/n（n+1）=1/n-1/（n+1）,原式就=1/100-1/101+1/101-1/102+1/102-1/103+.+1/149-1/150 =1/100-1/150 =1/300(1-1/2+1/3-1/4+...+1/99-1/100)/(1/101^2-1^2+1/102^2-2^2+...+1/150^2-50^2)_百度作业帮
(1-1/2+1/3-1/4+...+1/99-1/100)/(1/101^2-1^2+1/102^2-2^2+...+1/150^2-50^2)
(1-1/2+1/3-1/4+...+1/99-1/100)/(1/101^2-1^2+1/102^2-2^2+...+1/150^2-50^2)
分子=（1+1/2+1/3+1/4+……+1/99+1/100）-2*（1/2+1/4+……+1/100）=1+1/2+1/3+..+1/100-(1/1+1/2+1/3+...+1/50)=1/51+1/52+…+1/99+1/100分母=1/(100-1)(101+1)+1/(102-2)(102+2)+...+1/(150-50)(150+50)=1/100(1/102+1/104+...+1/200)=1/200(1/51+1/52+...+1/100)所以,原式=(1/51+1/52+…+1/99+1/100)/[1/200(1/51+1/52+...+1/100)]=1/(1/200)=200}