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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 - 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
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
A = 2⁵.(-5)² - 8² - 7
= 32.25 - 64 - 7
= 729
= 27²
B = 2³.(-4)² + (-3)².3² - 40
= 8.16 + 9.9 - 40
= 169
= 13²
C = (1/4 - 1/2 - 1)³ . (2 - 2/5)³
= (-5/4)³ . (8/5)³
= (-5/4 . 8/5)³
= (-2)³
D = (-1/4)² : (1/2 - 1/3)
= 1/16 : 1/6
= 3/8
E = 4 . (1/4)² + 25 . [(3/4)³ : (5/4)³] : (3/2)³
= 1/4 + 25 . (3/4 . 5/4)³ : (3/2)³
= 1/4 + 25 . (15/16)³ : 27/8
= 1/4 + 25 . 3375/4096 : 27/8
= 1/4 + 84375/4096 : 27/8
= 1/4 + 3125/512
= 3253/512
F = 2³ + 3.(1/2)⁰ - 1 + [(-2)² : 1/2] - 8
= 8 + 3.1 - 1 + (4 : 1/2) - 8
= 8 + 3 - 1 + 8 - 8
= 10
15: A= 1/3-3/4+3/5+1/2007-1/36+1/15-2/9
Sửa đề:
A=-3/4-2/9-1/36+1/3+3/5+1/15+1/2007
=-27/36-8/36-1/36+5/15+9/15+1/15+1/2007
=-1+1+1/2007=1/2007
16:
\(A=\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}-\dfrac{3}{4}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{64}\)
\(=\dfrac{5+9+1}{15}+\dfrac{-27-8-1}{36}+\dfrac{1}{64}\)
=1/64
17:
=1/2-1/2+2/3-2/3+3/4-3/4+4/5-4/5+5/6-5/6-6/7
=-6/7
`1-1/2+2-2/3+3-3/4-1/4-3-1/3-2-1/2-1`
`=(1+2+3-3-2-1)+(-1/2-2/3-3/4-1/4-1/3-1/2)`
`=(1+2+3-3-2-1)+[(-1/2 - 1/2)-(2/3-1/3)-(3/4 - 1/4)]`
`=0 + (-1 - 1 - 1)`
`=0 + (-3)`
`=0-3`
`=-3`
A = 1 -1/2 + 2 - 2/3 + 3 -3/4 -1/4 -3 -1/3 -2 -1/2 -1
A = ( 1 - 1/2 -1/2) + (2-2) + ( 3-3) - (2/3 -1/3) - (3/4+1/4) - 1
A = 0 + 0 + 0 -1 - 1-1
A = -3