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\(A=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+....+\frac{1}{1+2+3+...+49+50}\)
\(=\frac{1}{\frac{2.\left(2+1\right)}{2}}+\frac{1}{\frac{3.\left(3+1\right)}{2}}+\frac{1}{\frac{4.\left(4+1\right)}{2}}+.....+\frac{1}{\frac{50\left(50+1\right)}{2}}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+....+\frac{2}{50.51}\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{50}-\frac{1}{51}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{51}\right)=\frac{49}{51}\)
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Đặt \(A=1+2+2^2+...+2^{49}-\left(2^{50}+3\right)\)
\(B=1+2+2^2+...+2^{49}\)
\(\Rightarrow2B=2+2^2+2^3+...+2^{50}\)
\(\Rightarrow2B-B=\left(2+2^2+2^3+...+2^{50}\right)-\left(1+2+2^2+...+2^{49}\right)\)
\(\Rightarrow B=2^{50}-1\)
\(\Rightarrow A=2^{50}-1-\left(2^{50}+3\right)\)
\(\Rightarrow A=2^{50}-1-2^{50}-3\)
\(\Rightarrow A=\left(2^{50}-2^{50}\right)-\left(1+3\right)\)
\(\Rightarrow A=-4\)
Vậy A = -4
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Đặt A= 1+2+22+23+.............+249-(250+3)
B= 1+2+22+23+............+249
=> 2B=2+22+23+.....+250
=>2B-B= (2+22+23+.......+250) - (1+2+22 +.........+249)
=> B=250-1
=>A=250-1-(250+3)
=>A=250-1-250-3
=>A=(250-250)-(1+3) = -4
vậy giá trị của biểu thức A= -4
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a) \(87^2+26\cdot87+13^2=87^2+2\cdot87\cdot13+13^2=\left(87+13\right)^2=100^2=10000\)
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