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N
23 tháng 7 2015
a)\(A=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{48}}+\frac{1}{2^{49}}\)
\(A=1-\frac{1}{2^{50}}<1\)
Vậy \(A=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}<1\)
b)\(B=\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}+\frac{1}{3^{100}}\)
\(3B=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{98}}+\frac{1}{3^{99}}\)
\(3B-B=2B=1-\frac{1}{3^{100}}\)
\(B=\frac{1-\frac{1}{3^{100}}}{2}\)
Vì \(1-\frac{1}{3^{100}}<1\)nên\(\frac{1-\frac{1}{3^{100}}}{2}<\frac{1}{2}\)
Vậy \(B=\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}+\frac{1}{3^{100}}<\frac{1}{2}\)
c) \(C=\frac{1}{4^1}+\frac{1}{4^2}+\frac{1}{4^3}+...+\frac{1}{4^{999}}+\frac{1}{4^{1000}}\)
\(4C=1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{998}}+\frac{1}{4^{999}}\)
\(4C-C=3C=1-\frac{1}{4^{1000}}\)
\(C=\frac{1-\frac{1}{4^{1000}}}{3}\)
Vì \(1-\frac{1}{4^{1000}}<1\)nên\(\frac{1-\frac{1}{4^{1000}}}{3}<\frac{1}{3}\)
Vậy \(C=\frac{1}{4^1}+\frac{1}{4^2}+\frac{1}{4^3}+...+\frac{1}{4^{999}}+\frac{1}{4^{1000}}<\frac{1}{3}\)
DT
1
23 tháng 6 2016
1 - 1/2 + 2 - 2/3 + 3 - 3/4 + 4 - 1/4 - 3 - 1/3 - 2 - 1/2 - 1
= (1 - 1) - (1/2 + 1/2) + (2 - 2) - (2/3 + 1/3) + (3 - 3) - (3/4 + 1/4) + 4
= 0 - 1 + 0 - 1 + 0 - 1 + 4
= 0 - 3 + 4
= -3 + 4
= 1
F
1
F
5 tháng 9 2020
1) \(\left(\frac{3}{7}+\frac{1}{2}\right)^2=\left(\frac{13}{14}\right)^2=\frac{169}{196}\)
2) \(\left(\frac{3}{4}-\frac{5}{6}\right)^2=\left(-\frac{1}{12}\right)=\frac{1}{144}\)
3) \(\left(1+\frac{2}{3}-\frac{1}{4}\right)\cdot\left(\frac{4}{5}-\frac{3}{4}\right)^2\)
\(=\frac{17}{12}\cdot\left(\frac{1}{20}\right)^2=\frac{17}{4800}\)
4) \(2\div\left(\frac{1}{2}-\frac{2}{3}\right)^3=2\div\left(-\frac{1}{6}\right)^3\)
\(=2\div\left(-\frac{1}{216}\right)=-432\)
4 tháng 4 2020
1; = ( -4/10 + 3/10 ) : ( -2/5 + 2/3 ) = -1/10 : ( -6/15 + 10/15 ) = -1/10 : 4/15 = -1/10 . 15/4 = -15/40 = -3/8
2; = 25/2 . -5/7 + 39/4 + -3/2 . 5/7 = -125/14 + 39/4 + -15/14 = ( -125/14 + -15/14 ) + 39/4 = -10 + 39/4 = -40/4 + 39/4 = -1/4
3; = 5/52 + 35/52 + 40/52 = 40/52 + 40/52 = 80/52 = 20/13
4; = ( -39/52 + 20/52 ) . 7/2 - ( 117/52 + 32/52 ) . 7/2 = -19/52 . 7/2 - 149/52 . 7/2 = ( -19/52 + -149/52 ) . 7/2 = -168/52 .7/2 = -147/13
5; = ( 36/12 + -9/12 + 8/12 ) - ( -12/6 + -8/6 + -9/6 ) - ( 6/6 - 14/6 - 27/6 ) = 35/12 + 10/12 + 70/12 = 115/12
6; = -1/3 + -8/35 +-2/9 + -1/135 +4/5 +-4/9 +3/7 = (-1/3 + -2/9 + -4/9 ) + ( -8/35 + 4/5 + 3/7 ) + -1/135 = ( -1/3 + -2/3 ) + ( -8/35 + 28/35 + 15/35 ) + -1/135 = -1 + 1 + -1/135 = -1/135
PT
1
19 tháng 4 2020
1 - 1/2 + 2 - 2/3 + 3 - 3/4 + 4 - 1/4 - 3 - 1/3 - 2 - 1/2 - 1
=(1-1)+(2-2)+(3-3)+\(\left(-\frac{1}{2}-\frac{1}{2}\right)+\left(-\frac{2}{3}-\frac{1}{3}\right)+\left(\frac{-3}{4}-\frac{1}{4}\right)\)+4
=0+(-3)+4
=1