H=38/50+9/20-11/30+13/42-15/56+17/72-...+197/9702-199/9900

Đáp án: + Giải thích các bước giải:

`H=38/50+9/20-11/30+13/42-15/56+17/72-...+197/9702-199/9900`.

Ta có:

`9/20=9/(4*5)=1/4+1/5`.

`11/30=11/(6*5)=1/6+1/5`.
`...`.

`197/9702=197/(98*99)=1/98+1/99`.

`199/9900=199/(99*100)=1/99+1/100`.

`=>H=38/50+(1/4+1/5)-(1/6+1/5)-...+(1/98+1/99)-(1/99+1/100)`.

`=>H=38/50+1/4+1/5-1/6-1/5-...+1/98+1/99-1/99-1/100`.

`=>H=38/50+1/4+(1/5-1/5)-(1/6-1/6)-...+(-1/98+1/98)+(1/99-1/99)-1/100`.

`=>H=38/50+1/4-1/100`.

`=>H=1`.

Vậy:..