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

Question

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

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

1. 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)

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

= 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