Cho biểu thức A=1/3+1/3^2+1/3^3+1/3^4+...1/3^98+1/3^99. Chứng tỏ A<1/2
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Những câu hỏi liên quan
Cho A=1-3+3^2-3^3+...+3^98-3^99
a,Tính A
b,Chứng tỏ A chia hết cho -20
c,Chứng tỏ 3^100 chia 4 dư 1
Cho biểu thức A=3^99-3^98+3^97-3^96+....+3^3-3^2+3-1.Chứng tổ rằng A chia hết cho 4
giúp mình với
tính tổng
a, Biểu thức A=1*2+2*3+3*4+....+98*99
b, Biểu thức B=1 mũ 2 + 2 mũ 2 + 3 mũ 2+....+97 mũ 2 + 98 mũ 2
c, Biểu thức C=1*99+2*98+3*97*....*98*2+99*1
cho A=1/2-1/3+1/4-1/5+1/6-...-1/98-1/99
Chứng tỏ 0,2<A<0,4
Tính giá trị biểu thức
a, A = (1 - 1/1+2) . (1 - 1/1+2+3) . (1- 1/1+2+3+4) . ... .(1- 1/1+2+...+100)
b, B = (2/3+ 3/4 +...+99/100).(1/2+2/3+...+98/99) - (1/2+2/3+...+99/100).(2/3+3/4+...+98/99)
c, C = \(\frac{3^3+1^3}{2^3-1^3}+\frac{5^3+2^3}{3^3-2^3}+\frac{7^3+3^3}{4^3-3^3}+...+\frac{41^3+20^3}{21^3-20^3}\)
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a) thu gọn biểu thức sau: a= 5 - 5^2 + 5^3 - 5^4 +...- 5^98 + %^99
b) chứng minh rằng với mọi n thuộc N thì (2^n+1).(2^n+2) đều chia hết cho 3
c) chúng minh: A= 1/1^2 + 1/2^2+ 1/3^2+.....+1/99^2+ 1/100^2 < 1 3/4 (hỗn số)
Tính giá trị các biểu thức sau:
a) A = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100
b) B = 1 − 2 − 3 + 4 + 5 − 6 − 7 + ... + 97 − 98 − 99 + 100
a)
C = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100 = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100 = − 1 + − 1 + ... + − 1 + − 1 = − 1.50 = − 50.
b)
B = 1 − 2 − 3 + 4 + 5 − 6 − 7 + ... + 97 − 98 − 99 + 100 = 1 − 2 + − 3 + 4 + 5 − 6 + ... + 97 − 98 + − 99 + 100 = − 1 + 1 + − 1 + ... + − 1 + 1 = − 1 + 1 + − 1 + 1 + ... + − 1 + 1 − 1 = 0 + 0 + ... + 0 − 1 = − 1.
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Cho A=\(\frac{4}{3}+\frac{10}{3^2}+\frac{28}{3^2}+...+\)\(\frac{3^{98}+1}{3^{98}}\).Chứng tỏ :98 < A < 99
A=\(\frac{4}{3}+\frac{10}{3^2}+...+\frac{3^{98}+1}{3^{98}}\)
=> A>\(\frac{3}{3}+\frac{9}{9}+...+\frac{3^{98}}{3^{98}}\) = 1+1+..+1 =98
A=\(\frac{3}{3}+\frac{9}{9}+...+\frac{3^{98}}{3^{98}}\) +\(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{98}}\)> 1+1+..+1 = 98
Đặt B = \(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{98}}\)
=> 3B = \(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{97}}\)
=>2B = 1-\(\frac{1}{3^{98}}\) <1
=> B<1
=>A<99
=>98<A<99
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DX
2 tháng 7 2021 lúc 21:10
Tính giá trị biểu thức A , biết rằng A M : N Mà M dfrac{dfrac{1}{99}+dfrac{2}{98}+dfrac{3}{97}+dfrac{4}{96}+...+dfrac{97}{3}+dfrac{98}{2}+dfrac{99}{1}}{dfrac{1}{2}+dfrac{1}{3}+dfrac{1}{4}+dfrac{1}{5}+dfrac{1}{6}+...+dfrac{1}{100}} N dfrac{92-dfrac{1}{9}-dfrac{2}{10}-dfrac{3}{11}-...-dfrac{90}{98}-dfrac{91}{99}-dfrac{92}{100}}{dfrac{1}{45}+dfrac{1}{50}+dfrac{1}{55}+...+dfrac{1}{495}+dfrac{1}{500}}
Đọc tiếp
Tính giá trị biểu thức A , biết rằng A = M : N
Mà M = \(\dfrac{\dfrac{1}{99}+\dfrac{2}{98}+\dfrac{3}{97}+\dfrac{4}{96}+...+\dfrac{97}{3}+\dfrac{98}{2}+\dfrac{99}{1}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{100}}\)
N = \(\dfrac{92-\dfrac{1}{9}-\dfrac{2}{10}-\dfrac{3}{11}-...-\dfrac{90}{98}-\dfrac{91}{99}-\dfrac{92}{100}}{\dfrac{1}{45}+\dfrac{1}{50}+\dfrac{1}{55}+...+\dfrac{1}{495}+\dfrac{1}{500}}\)
Ta có: \(M=\dfrac{\dfrac{1}{99}+\dfrac{2}{98}+\dfrac{3}{97}+\dfrac{4}{96}+...+\dfrac{97}{3}+\dfrac{98}{2}+\dfrac{99}{1}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{100}}\)
\(=\dfrac{\left(1+\dfrac{1}{99}\right)+\left(1+\dfrac{2}{98}\right)+\left(1+\dfrac{3}{97}\right)+\left(1+\dfrac{4}{96}\right)+...+\left(1+\dfrac{98}{2}\right)+1}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{100}}\)
\(=\dfrac{\dfrac{100}{99}+\dfrac{100}{98}+\dfrac{100}{97}+...+\dfrac{100}{1}+\dfrac{100}{2}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{100}}\)
=100
Ta có: \(N=\dfrac{92-\dfrac{1}{9}-\dfrac{2}{10}-\dfrac{3}{11}-...-\dfrac{90}{98}-\dfrac{91}{99}-\dfrac{92}{100}}{\dfrac{1}{45}+\dfrac{1}{50}+\dfrac{1}{55}+...+\dfrac{1}{495}+\dfrac{1}{500}}\)
\(=\dfrac{\left(1-\dfrac{1}{9}\right)+\left(1-\dfrac{2}{10}\right)+\left(1-\dfrac{3}{11}\right)+...+\left(1-\dfrac{90}{98}\right)+\left(1-\dfrac{91}{99}\right)+\left(1-\dfrac{92}{100}\right)}{\dfrac{1}{5}\left(\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}+...+\dfrac{1}{99}+\dfrac{1}{100}\right)}\)
\(=\dfrac{\dfrac{8}{9}+\dfrac{8}{10}+\dfrac{8}{11}+...+\dfrac{8}{99}+\dfrac{8}{100}}{\dfrac{1}{5}\left(\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{11}+...+\dfrac{1}{99}+\dfrac{1}{100}\right)}\)
\(=\dfrac{8}{\dfrac{1}{5}}=40\)
\(\Leftrightarrow\dfrac{M}{N}=\dfrac{100}{40}=\dfrac{5}{2}\)
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