Chứng tỏ răng: 9/2.5+9/5.8+9/8.11+………+9/29.32 >1

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Chứng tỏ răng: 9/2.5+9/5.8+9/8.11+………+9/29.32 >1

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Peyton 1 tháng 2021-08-31T17:49:38+00:00 2 Answers 7 views 0

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    0
    2021-08-31T17:50:42+00:00

    `9/(2.5)+9/(5.8)+9/(8.11)+………+9/(29.32)`

    `= 3 . (3/(2.5)+3/(5.8)+3/(8.11)+………+3/(29.32))`

    `= 3 . (1/2 – 1/5 + 1/5 – 1/8 + 1/8 – 1/11 + …+1/29 – 1/32)`

    `= 3 . (1/2-1/32)`

    `= 3. 15/32`

    `= 45/32 > 1`

    Vậy `9/(2.5)+9/(5.8)+9/(8.11)+………+9/(29.32) > 1`

    (Chúc bạn học tốt)

    0
    2021-08-31T17:51:01+00:00

    $\frac{9}{2.5}$ + $\frac{9}{5.8}$ + $\frac{9}{8.11}$ + … + $\frac{9}{29.32}$

    = 3.$\frac{3}{2.5}$ + 3.$\frac{3}{5.8}$ + 3.$\frac{3}{8.11}$ + … + 3.$\frac{3}{29.32}$

    = 3.($\frac{1}{2}$ – $\frac{1}{5}$ + $\frac{1}{5}$ – $\frac{1}{8}$ + $\frac{1}{8}$ – $\frac{1}{11}$ + … + … $\frac{1}{29}$ – $\frac{1}{32}$)

    = 3.($\frac{1}{2}$ – $\frac{1}{32}$)

    = 3.($\frac{16}{32}$ – $\frac{1}{32}$)

    = 3.$\frac{15}{32}$

    = $\frac{45}{32}$

    mà $\frac{45}{32}$ = 1$\frac{13}{32}$ 

    mà 1$\frac{13}{32}$ > 1

    ⇒$\frac{9}{2.5}$ + $\frac{9}{5.8}$ + $\frac{9}{8.11}$ + … + $\frac{9}{29.32}$ > 1

     

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