Đáp án:
Giải thích các bước giải:
a,S=`1/4.7+1/7.10+. . .+1/19.22`
=`1/3`.`(3/4.7+3/7.10+. . .+3/19.22)`
= `1/3`.`(1/4-1/7+1/7-1/10+. . .+1/19-1/22)`
=`1/3` . `(1/4-1/22)`
=`1/3`.`9/44`
=`3/44`
b,S=`1/1.7+1/7.13+. . .+1/25.31`
S = `1/6`.`(6/1.7+6/7.13+. . .+6/25.31)`
S = `1/6` . ` (1-1/7+1/7-1/13+. . .+1/25-1/31)`
S = `1/6` . `(1-1/31)`
S = `1/6`.`30/31`
S = `5/31`
c,S=`2/6`+`2/12`+`2/20`+. . .+`2/90`
S= 2.`(1/6+1/12+. . .+1/90)`
S=2.`(1/2.3+1/3.4+. . .+1/9.10)`
S=2.`(1/2-1/3+1/3-1/4+. . .+1/9-1/10`)
S=2.`(1/2-1/10)`
S=2.`2/5`
S=`4/5`
d,S = `1/10`+`1/40`+`1/88`+. . .+`1/340`
S = `1/2.5`+`1/5.8`+`1/8.11`+. . .+ `1/17.20`
S = `1/3`.`(3/2.5`+`3/5.8`+`3/8.11`+. . .+ `3/17.20)`
S=`1/3`.`(1/2-1/5+1/5-1/8+1/8-1/11+. . .+1/17-1/20)`
S=`1/3`.`(1/2-1/20)`
S=`1/3`.`9/20`
S =`3/20`