Đáp án:
`A = 33/100` ; `B=49/100` ; `C= 5/14`
Giải thích các bước giải:
A = `1/3 . 3. (1/(1.4) + 1/(4.7) + ..... + 1/(97. 100))`
`= 1/3 . ( 3/(1.4) + 3/(4.7) +...+ 3/(97.100))`
`= 1/3. ( 1 - 1/4 + 1/4 - 1/7+...+ 1/97 - 1/100 )`
`= 1/3 . (1- 1/100)`
`= 1/3 . 99/100`
`= 33/100`
Vậy `A= 33/100`
B `= 5/(2.4) + 5/(4.6) + ....+ 5/(98.100)`
`=1/2 . 5 . 2 . [1/(2.4 ) + 1/(4.6) +. .....+ 1/(98. 100)]`
`= 5/2 . [2/(2.4) + 2/(4.6 ) + ...+ 2/(98.100) ]`
`= 5/2 . (1/2 - 1/4 + 1/4 - 1/6 + ....+ 1/98- 1/100)`
`= 5/2 . (1/2 - 1/100)`
`= 5/2 . 49/100`
`= 49/40`
Vậy `B= 49/40`
`C = 10/56 + 10/140 + 10/260 + ...+ 10/1400`
`= 5/28 + 5/70 + ....+ 5/700`
`= 5/(4.7) + 5/(7.10) + ... + 5/(25.28)`
`= 5 . 1/3 . 3 . [ 1/(4.7) + 1/(7.10) + ...+ 1/(25.28) ]`
`= 5/3 . [ 3/ (4.7) + 3/(7.10) +...+ 3/(25.28)]`
`= 5/3. (1/4 - 1/7+ 1/7 - 1/10+...+ 1/25 - 1/28)`
`= 5/3 . (1/4 - 1/28)`
`= 5/3. 6/28`
`= 5/3. 3/14`
`= 5/14`
Vậy `C = 5/14`
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