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mk pít lm phần a nhưng k có thời gian
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Chứng minh rằng :
a) \(\dfrac{1}{2!}+\dfrac{1}{3!}+\dfrac{1}{4!}+...+\dfrac{1}{100!}< 1\)
b) \(\dfrac{9}{10!}+\dfrac{9}{11!}+\dfrac{9}{12!}+...+\dfrac{9}{1000!}< \dfrac{1}{9!}\)
Cho A= \(\dfrac{1}{5^2}+\dfrac{2}{5^3}+\dfrac{3}{5^4}+...+\dfrac{11}{5^{12}}\) với n\(\in N\)
Chứng minh rằng a < \(\dfrac{1}{16}\)
Cho Cdfrac{1}{11}+dfrac{1}{12}+dfrac{1}{13}+...+dfrac{1}{70}
Chứng minh rằng : dfrac{4}{3} C 2,5
Giúp mk vs ..............
Đọc tiếp
Cho \(C=\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+...+\dfrac{1}{70}\)
Chứng minh rằng : \(\dfrac{4}{3}< C< 2,5\)
Giúp mk vs .............. 
2 Chứng minh:
a) \(\dfrac{1}{n}.\dfrac{1}{n+4}=\dfrac{1}{4}.(\dfrac{1}{n}-\dfrac{1}{n+4})\) b)Tính A=\(\dfrac{4}{3}.\dfrac{4}{7}+\dfrac{4}{7}.\dfrac{4}{11}+...+\dfrac{4}{95}.\dfrac{4}{99}\)
Chứng minh rằng các tổng sau không phải là số tự nhiên :
a) \(A=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}\)
b) \(B=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{8}\)
c) \(C=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{16}\)
a) (0,75 - 1/4): 5/6
b) (3/4-0,25):3/7
c)1 dfrac{13}{15}.(0.5)^2 .3+(8/15- 1dfrac{19}{60}):1dfrac{23}{24}
d) (3dfrac{1}{3}+2,5):(3dfrac{1}{6}-4dfrac{1}{5})-dfrac{11}{31}
e) [6+(1/2)^3- /-dfrac{1}{2}/ ] :3/12
Đọc tiếp
a) (0,75 - 1/4): 5/6
b) (3/4-0,25):3/7
c)1 \(\dfrac{13}{15}\).(0.5)^2 .3+(8/15- 1\(\dfrac{19}{60}\)):1\(\dfrac{23}{24}\)
d) (3\(\dfrac{1}{3}\)+2,5):(3\(\dfrac{1}{6}\)-4\(\dfrac{1}{5}\))-\(\dfrac{11}{31}\)
e) [6+(1/2)^3- /-\(\dfrac{1}{2}\)/ ] :3/12
1.So Sánh
a) A=\(\dfrac{11}{2017}+\dfrac{4}{2019}và\) B=\(\dfrac{10}{2017}+\dfrac{10}{2019}\)
b) M=\(\dfrac{1}{5}+\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{30}+\dfrac{1}{61}+\dfrac{1}{62}và\dfrac{1}{2}\)
c) E=\(\dfrac{4116-14}{10290-35}và\) K=\(\dfrac{2929-101}{2.1919+404}\)
BT1: CMR:
a) dfrac{1}{2^2}+dfrac{1}{3^2}+dfrac{1}{4^2}+...+dfrac{1}{n^2} 1
b) dfrac{1}{4}+dfrac{1}{16}+dfrac{1}{36}+dfrac{1}{64}+dfrac{1}{100}+dfrac{1}{144}+dfrac{1}{196} dfrac{1}{2}
c) dfrac{1}{3}+dfrac{1}{30}+dfrac{1}{32}+dfrac{1}{35}+dfrac{1}{45}+dfrac{1}{47}+dfrac{1}{50} dfrac{1}{2}
d) dfrac{1}{2}-dfrac{1}{4}+dfrac{1}{8}-dfrac{1}{16}+dfrac{1}{32}-dfrac{1}{64} dfrac{1}{3}
e) dfrac{1}{3} dfrac{2}{3^2}+dfrac{3}{3^3}-dfrac{4}{3^4}+...+dfrac{99}{3^{99}}-dfrac{100}{3^{100}} dfrac{3}{16}
f) d...
Đọc tiếp
BT1: CMR:
a) \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{n^2}< 1\)
b) \(\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{36}+\dfrac{1}{64}+\dfrac{1}{100}+\dfrac{1}{144}+\dfrac{1}{196}< \dfrac{1}{2}\)
c) \(\dfrac{1}{3}+\dfrac{1}{30}+\dfrac{1}{32}+\dfrac{1}{35}+\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{50}< \dfrac{1}{2}\)
d) \(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}< \dfrac{1}{3}\)
e) \(\dfrac{1}{3}< \dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}< \dfrac{3}{16}\)
f) \(\dfrac{1}{41}+\dfrac{1}{42}+\dfrac{1}{43}+...+\dfrac{1}{79}+\dfrac{1}{80}>\dfrac{7}{12}\)
BT2: Tính tổng
a) A=\(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{100}}\)
b) E=\(1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+\dfrac{1}{4}\left(1+2+3+4\right)+...+\dfrac{1}{200}\left(1+2+3+...+200\right)\)
BT3: Cho S=\(\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}\)
CMR: 1 < S < 2
So sánh: A=\(\dfrac{1}{2}+\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}\)với 0,9