OPTADS360
ATNETWORK
RANDOM
ON
YOMEDIA
Banner-Video
IN_IMAGE

Chứng tỏ 1/11+1/12+1/13+...+1/69+1/70 > 1+5/29

chứng tỏ rằng : 1https:https://hoc247.net/image/faq/data2/216985_.https://hoc247.net/image/faq/data2/216985_.hoc247.nethttps://hoc247.net/image/faq/data2/216985_.imagehttps://hoc247.net/image/faq/data2/216985_.faqhttps://hoc247.net/image/faq/data2/216985_.data2https://hoc247.net/image/faq/data2/216985_.563596_.11+1https:https://hoc247.net/image/faq/data2/216985_.https://hoc247.net/image/faq/data2/216985_.hoc247.nethttps://hoc247.net/image/faq/data2/216985_.imagehttps://hoc247.net/image/faq/data2/216985_.faqhttps://hoc247.net/image/faq/data2/216985_.data2https://hoc247.net/image/faq/data2/216985_.563596_.12+1https:https://hoc247.net/image/faq/data2/216985_.https://hoc247.net/image/faq/data2/216985_.hoc247.nethttps://hoc247.net/image/faq/data2/216985_.imagehttps://hoc247.net/image/faq/data2/216985_.faqhttps://hoc247.net/image/faq/data2/216985_.data2https://hoc247.net/image/faq/data2/216985_.563596_.13+...+1https:https://hoc247.net/image/faq/data2/216985_.https://hoc247.net/image/faq/data2/216985_.hoc247.nethttps://hoc247.net/image/faq/data2/216985_.imagehttps://hoc247.net/image/faq/data2/216985_.faqhttps://hoc247.net/image/faq/data2/216985_.data2https://hoc247.net/image/faq/data2/216985_.563596_.69+1https:https://hoc247.net/image/faq/data2/216985_.https://hoc247.net/image/faq/data2/216985_.hoc247.nethttps://hoc247.net/image/faq/data2/216985_.imagehttps://hoc247.net/image/faq/data2/216985_.faqhttps://hoc247.net/image/faq/data2/216985_.data2https://hoc247.net/image/faq/data2/216985_.563596_.70>1+5https:https://hoc247.net/image/faq/data2/216985_.https://hoc247.net/image/faq/data2/216985_.hoc247.nethttps://hoc247.net/image/faq/data2/216985_.imagehttps://hoc247.net/image/faq/data2/216985_.faqhttps://hoc247.net/image/faq/data2/216985_.data2https://hoc247.net/image/faq/data2/216985_.563596_.29

Ai làm đúng và nhanh nhất mình sẽ tick max điểm

  bởi Mai Đào 13/11/2018
AMBIENT-ADSENSE/lession_isads=0
QUẢNG CÁO
 

Câu trả lời (1)

  • Gọi \(\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+...+\dfrac{1}{69}+\dfrac{1}{70}\) là \(S\)

    Ta nhận thấy:

    \(\dfrac{1}{11},\dfrac{1}{12},\dfrac{1}{13},...,\dfrac{1}{19}\)đều lớn hơn \(\dfrac{1}{20}\)

    \(\dfrac{1}{21},\dfrac{1}{22},\dfrac{1}{23},...,\dfrac{1}{29}\)đều lớn hơn \(\dfrac{1}{30}\)
    \(\dfrac{1}{31},\dfrac{1}{32},\dfrac{1}{33},...,\dfrac{1}{39}\)đều lớn hơn \(\dfrac{1}{40}\)
    \(\dfrac{1}{41},\dfrac{1}{42},\dfrac{1}{43},...,\dfrac{1}{49}\)đều lớn hơn \(\dfrac{1}{50}\)
    \(\dfrac{1}{51},\dfrac{1}{52},\dfrac{1}{53},...,\dfrac{1}{59}\)đều lớn hơn \(\dfrac{1}{60}\)

    \(\dfrac{1}{61},\dfrac{1}{62},\dfrac{1}{63},...,\dfrac{1}{69}\)đều lớn hơn \(\dfrac{1}{70}\)

    \(\Rightarrow S< \dfrac{1}{20}+\dfrac{1}{20}+...+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{30}+...+\dfrac{1}{30}+\dfrac{1}{40}+\dfrac{1}{40}+...+\dfrac{1}{40}+\dfrac{1}{50}+\dfrac{1}{50}+...+\dfrac{1}{50}+\dfrac{1}{60}+\dfrac{1}{60}+...+\dfrac{1}{60}+\dfrac{1}{70}+\dfrac{1}{70}+...+\dfrac{1}{70}\\ \Leftrightarrow S< \dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}\\ =\dfrac{223}{140}\)
    \(1\dfrac{5}{29}=\dfrac{34}{29}\)
    \(\dfrac{223}{140}>\dfrac{210}{140}=\dfrac{3}{2}=\dfrac{87}{58}>\dfrac{34}{29}\)
    Vậy \(\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+...+\dfrac{1}{69}+\dfrac{1}{70}>1+\dfrac{5}{29}\left(đpcm\right)\)
      bởi Chu Hồng Nhung 13/11/2018
    Like (0) Báo cáo sai phạm
Cách tích điểm HP

Nếu bạn hỏi, bạn chỉ thu về một câu trả lời.
Nhưng khi bạn suy nghĩ trả lời, bạn sẽ thu về gấp bội!

Lưu ý: Các trường hợp cố tình spam câu trả lời hoặc bị báo xấu trên 5 lần sẽ bị khóa tài khoản

Gửi câu trả lời Hủy
 
 

Các câu hỏi mới

NONE
OFF

XEM NHANH CHƯƠNG TRÌNH LỚP 6