Question

Cho tổng : S = \(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{60}\) . Chứng minh : \(\dfrac{3}{5}< S< \dfrac{4}{5}\)

Giúp mik vs các bn ơi ! Đúng + nhanh nhất = tick ...... Mơn trước !

Answer 1

S sẽ có 30 số hạng. Nhóm thành 3 nhóm, mỗi nhóm 101 số hạng.

S= (1/31+1/32+...+1/40) + (1/41 + 1/42 +...+1/50) + (1/51 +1/52+...+1/60)

S < (1/30 + 1/30 +...+ 1/30) + ( 1/40 +1/40+...+1/40) + (1/50 +1/50+...+1/50)

S < 1/30 + 1/40 +1/50 ; S < 47/60 < 48/60 = 4/5 (1)

S > (1/40 + 1/40 +...=1/40) + (1/50 + 1/50 +...+1/50) + (1/60 +1/60+...+1/60)

S < 10/40 + 10/50 +10/60 ; S > 37/60 > 36/60 = 3/5 (2)

Tư (1) và (2) => 3/5 < S < 4/5

NHỚ TICK CHO MINK NHA, CHÚC BẠN HỌC TỐT

Answer 2

S=(\(\dfrac{1}{31}\)+\(\dfrac{1}{32}\)+...+\(\dfrac{1}{40}\))+(\(\dfrac{1}{41}\)+\(\dfrac{1}{42}\)+...+\(\dfrac{1}{50}\))+(\(\dfrac{1}{51}\)+\(\dfrac{1}{52}\)+...+\(\dfrac{1}{60}\))

=>\(\dfrac{10}{40}\)+\(\dfrac{10}{50}\)+\(\dfrac{10}{60}\)< S < \(\dfrac{10}{30}\)+\(\dfrac{10}{40}\)+\(\dfrac{10}{50}\)

=>\(\dfrac{37}{60}\)< S <\(\dfrac{47}{60}\)

=>\(\dfrac{3}{5}\)=\(\dfrac{36}{60}\)<\(\dfrac{37}{60}\)< S < \(\dfrac{47}{60}\)<\(\dfrac{48}{60}\)=\(\dfrac{4}{5}\)

=> \(\dfrac{3}{5}\)< S <\(\dfrac{4}{5}\)