tính nhanh
1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + 1/5×6 + 1/6×7 + …. + 1/9×10 + 1/10×11
tính nhanh 1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + 1/5×6 + 1/6×7 + …. + 1/9×10 + 1/10×11
By aihong
By aihong
tính nhanh
1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + 1/5×6 + 1/6×7 + …. + 1/9×10 + 1/10×11
Đáp án:
Giải thích các bước giải:
1 1 + 1 1 1 1 1 1
— + — + — + — + — + — + …. + — + —
1 x 2 2 x 3 3 x 4 4 x 5 5 x 6 6 x 7 9 x 10 10 x 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
=1- — + — – — + — – — + — – — + — – — + — – — + …. + — – — + — – —
2 2 3 3 4 4 5 5 6 6 7 9 10 10 11
1
= 1 – —
11
10
= —
11
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cho xin câu trả lời hay nhứt ngoa
ta có :
`\frac{1}{1 xx 2} = 1 – 1/2`
`\frac{1}{2 xx 3} = 1/2 – 1/3`
`\frac{1}{3 xx 4} = 1/3 – 1/4`
`\frac{1}{4xx5} = 1/4 – 1/5`
`\frac{1}{5xx6}= 1/5 – 1/6`
`\frac{1}{6xx7} = 1/6 – 1/7`
…………….
`\frac{1}{9 xx 10} = 1/9 – 1/10`
`\frac{1}{10xx11} = 1/10 – 1/11`
⇒`\frac{1}{1 xx 2} +\frac{1}{2 xx 3} + \frac{1}{3 xx 4}+ \frac{1}{4xx5} +\frac{1}{5xx6} + \frac{1}{6xx7} + ……. +\frac{1}{9 xx 10} +\frac{1}{10xx11}`
`=1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + 1/6 – 1/7 + ….. + 1/9 – 1/10 + 1/10 – 1/11`
`= 1 – 1/11`
`= 11/11 – 1/11`
`= 10/11`