S=(1/31+1/32+...+1/40)+(1/41+...+1/50)+(1/51+...+1/60)
=>S>1/40*10+1/50*10+1/60*10=3/5
S=(1/31+1/32+...+1/40)+(1/41+...+1/50)+(1/51+...+1/60)
=>S<1/30*10+1/40*10+1/50*10=4/5
=>3/5<S<4/5
Cho tổng S= \(\dfrac{1}{31}\) + \(\dfrac{1}{32}\) + ... + \(\dfrac{1}{60}\) Chứng minh \(\dfrac{3}{5}\) < S < \(\dfrac{4}{5}\)
b, Cho tổng : \(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{60}\) Chứng minh \(\dfrac{3}{5}< S< \dfrac{4}{5}\)
b, Cho tổng : \(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{60}\) .Chứng minh: \(\dfrac{3}{5}< S< \dfrac{4}{5}\)
Cho S = \(\dfrac{1}{31}\) + \(\dfrac{1}{32}\) + \(\dfrac{1}{33}\) + ... + \(\dfrac{1}{60}\). Chứng minh rằng: S < \(\dfrac{4}{5}\)
Chứng minh S<\(\dfrac{5}{32}\)
Cho \(S=\dfrac{1}{5^2}+\dfrac{1}{7^2}+...+\dfrac{1}{103^2}\)
1. Cho N=\(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{60}\)
CMR \(\dfrac{3}{5}< N< \dfrac{4}{5}\)
2. Cho M=\(\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{29}{3^{29}}-\dfrac{30}{3^{30}}\)
CMR \(M< \dfrac{3}{16}\)
3. Cho Q=\(\dfrac{2}{3}+\dfrac{8}{9}+\dfrac{26}{27}+...+\dfrac{3^{2021}-1}{3^{2021}}\)
CMR \(Q>\dfrac{4041}{2}\)
a)chứng minh rằng :\(\dfrac{1}{3^2}\)+\(\dfrac{1}{4^2}\)+\(\dfrac{1}{5^2}\)+\(\dfrac{1}{6^2}\)........+\(\dfrac{1}{100^2}< \dfrac{1}{2}\)
b)tính nhanh tổng S với S= \(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+......+\dfrac{1}{61.63}\)
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Cho \(S=\dfrac{1}{5^2}+\dfrac{2}{5^3}+\dfrac{3}{5^4}+...+\dfrac{99}{5^{100}}\). Chứng tỏ rằng S<\(\dfrac{1}{16}\)
Cho S=\(\dfrac{1}{5^2}+\dfrac{2}{5^3}+\dfrac{3}{5^4}+...+\dfrac{99}{5^{100}}\) . Chứng tỏ rằng \(S< \dfrac{1}{16}\)
