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Vì 1=\((1)^{2}\)=\((1)^{3}\)=....
Nên tất cả các tích ở B đều có giá trị bằng 1
=> B = 1.1.1.1....1 = 1
Đặt \(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)
\(\Rightarrow2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)
\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2011}}+\frac{1}{2^{2012}}\)
\(\Rightarrow2A-A=A=2-\frac{1}{2^{2012}}\)
\(a.\frac{4.7}{9.32}=\frac{4.7}{4.8.9}=\frac{7}{8.9}=\frac{7}{72}\)
\(b.\frac{990}{2610}=\frac{990\div90}{2610\div90}=\frac{11}{29}\)
\(c.\frac{374}{-506}=\frac{374\div\left(-22\right)}{-506\div\left(-22\right)}=\frac{-17}{23}\)
\(\frac{4\cdot7}{9\cdot32}=\frac{4\cdot7}{9\cdot4\cdot8}=\frac{7}{9\cdot8}=\frac{7}{72}\)
\(\frac{990}{2610}=\frac{2\cdot3^2\cdot5\cdot11}{2\cdot3^2\cdot5\cdot29}=\frac{11}{29}\)
\(\frac{374}{-506}=-\frac{374}{506}=\frac{2\cdot11\cdot17}{2\cdot11\cdot23}=-\frac{17}{23}\)
A=22 + 24 + 26 +...+ 230
2A=24 + 26 + 28+...+231
2A-A=(24 + 26 + 28+...+231)-(22 + 24 + 26 +...+ 230)
A=231-22
Tick nha
a, A = 3/2 × 4/3 × 5/4 × ... × 81/80
A = 81/2
b) (1 - 1/2) × (1 - 1/3) × ... × (1 - 1/100)
= 1/2 × 2/3 × .. × 99/100
= 1/100
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+.......+\frac{1}{2^{99}}\)
\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+.......+\frac{1}{2^{99}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.......+\frac{1}{2^{100}}\right)\)
\(A=1-\frac{1}{2^{100}}\)
\(A=\frac{2^{100}-1}{2^{100}}\)
B=\(2003^{2^{0^{1^0}}}=2003^{2^{0^1}}=2003^{2^0}=2003^1=2003\)
B = 20032010 = 2003201 = 200320 = 20031 = 2003