Ta có: \(S< \dfrac{1}{2}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{31}+\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{32}\) \(=\dfrac{1}{2}+\dfrac{3}{11}+\dfrac{2}{31}+\dfrac{2}{32}\)
\(=\dfrac{4909}{5456}< \dfrac{9}{10}\)
\(\Rightarrow S< \dfrac{9}{10}\)
Vậy \(S< \dfrac{9}{10}\)
BT5 : Chứng minh
2) \(\dfrac{3}{5}< \dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+....+\dfrac{1}{59}+\dfrac{1}{60}< \dfrac{4}{5}\)
Chứng minh :
\(\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{60}=\dfrac{1}{1.2}+\dfrac{1}{3.4}+..+\dfrac{1}{59.60}\)
Cho S = \(\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{16}+\dfrac{1}{17}+\dfrac{1}{18}+\dfrac{1}{19}+\dfrac{1}{20}\). Hãy so sánh S và \(\dfrac{1}{2}\)
Cho S=\(\dfrac{1}{31}\)+\(\dfrac{1}{32}\)+\(\dfrac{1}{33}\)+.....+\(\dfrac{1}{60}\)
CMR:\(\dfrac{3}{5}\)<S<\(\dfrac{4}{5}\)
Cho S =\(\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{16}+\dfrac{1}{17}+\dfrac{1}{18}+\dfrac{1}{19}+\dfrac{1}{20}\)
Hãy so sánh S và \(\dfrac{1}{2}\)
Các bạn giúp mình nhé mình đang cần gấp
Cho \(S=\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+..............+\dfrac{1}{20}\). So sánh \(S\) và \(\dfrac{7}{12}\)
1, Tính:
a, A = \(\dfrac{24.47-23}{24.47-23}\).\(\dfrac{3.\dfrac{3}{7}-\dfrac{3}{31}+\dfrac{3}{1001}-\dfrac{3}{13}}{\dfrac{9}{1001}-\dfrac{9}{15}+\dfrac{9}{7}-\dfrac{9}{11}+9}\)
b, B = 1 + 2 + 2\(^2\) + 2\(^3\) + .....+ 2 \(^{2013}\)
Cho \(S=\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+...........+\dfrac{1}{20}\) Hãy so sánh \(S\) và \(\dfrac{7}{12}\)
Help me!!!!!!!!!
1. Tính giá trị biểu thức:
M=\(1+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{100}}\)
2.Chứng tỏ rằng :
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< 1\)
3.So sánh
a, A=\(\dfrac{11^5+1}{11^6+1}\) ; B=\(\dfrac{11^6+1}{11^7+1}\)
b, M=\(\dfrac{15^{10}-1}{15^9+1}\) ; N=\(\dfrac{15^9-1}{15^{10}+1}\)