Giải thích các bước giải:
h) Ta có:
`1/1.4+1/4.7+...+1/(x.(x+1))=125/376`
`=>3(1/1.4+1/4.7+...+1/(x.(x+1)))=3. 125/376`
`=>3/1.4+3/4.7+...+1/(x.(x+1))=375/376`
`=>1-1/4+1/4-1/7+...+1/x-1/(x+1)=375/376`
`=>1-1/(x+1)=375/376`
`=>1/(x+1)=1-375/376=1/376`
`=>x+1=376`
`=>x=375.`
k) Ta có:
`1/3+1/6+1/10+1/15+...+1/(x.(2x+1))=1/10`
`=>1/2(1/3+1/6+1/10+1/15+...+1/(x.(2x+1)))=1/2. 1/10`
`=>1/6+1/12+1/20++1/30+...+1/(x.(x+1))=1/20`
`=>1/2.3+1/3.4+1/4.5+1/5.6+...+1/(x.(x+1))=1/20`
`=>1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/x-1/(x+1)=1/20`
`=>1/2-1/(x+1)=1/20`
`=>1/(x+1)=1/2-1/20=9/20`
`=>9(x+1)=20`
`=>9x+9=20`
`=>9x=11`
`=>x=11/9.`
j) Ta có:
`1/15+1/21+1/28+1/36+...+2/(x.(x+1))=11/40`
`=>1/2(1/15+1/21+1/28+1/36+...+1/(x.(x+1)))=1/2. 11/40`
`=>1/30+1/42+1/56+1/72+...+1/(x.(x+1))=11/80`
`=>1/5.6+1/6.7+1/7.8+1/8.9+...+1/(x.(x+1))=11/80`
`=>1/5-1/6+1/6-1/7+1/7-1/8+...+1/x-1/(x+1)=11/80`
`=>1/5-1/(x+1)=11/80`
`=>1/(x+1)=1/5-11/80=5/80=1/16`
`=>x+1=16`
`=>x=15.`
