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\(S=1+\frac{1}{2}+1+\frac{1}{4}+1+\frac{1}{8}+1+\frac{1}{16}+1+\frac{1}{32}+1+\frac{1}{64}-7\)
\(S=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}-1\)
Ta đặt: \(P=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
=> \(2P=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
=> \(2P-P=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
=> \(P=1-\frac{1}{64}\)
Mà \(S=P-1\)
=> \(S=1-\frac{1}{64}-1=-\frac{1}{64}\)
Vậy \(S=-\frac{1}{64}\)
N = 3/2 + 5/4 + 9/8 + 17/16 + 33/32 + 65/64 - 7
N = (1 + 1/2) + (1 + 1/4) + (1 + 1/8) + (1 + 1/16) + (1 + 1/32) + (1 + 1/64) - 7
N = (1 + 1 + 1 + 1 + 1 + 1 ) + (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64) - 7
N = 6 - (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64) - 7
Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64
2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32
2A - A = (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32) - (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)
A = 1 - 1/64
N = 6 - (1 - 1/64) - 7
N = 6 - 1 + 1/64 - 7
N = 5 + 1/64 - 7
N = -2 + 1/64
N = -128/64 + 1/64
N = -127/64
bạn soyen_Tiểu bàng giải sao dòng 3 đang cộng đến dòng 9 lại chuyển thành trừ vậy
a) (-37) + 14 + 26 + 37
= [(-37) + 37] + (14 + 26)
= 0 + 40 = 40
b) (-24) + 6 + 10 + 24
= [(-24) + 24] + (10 + 6)
= 0 + 16 = 16
c) 15 + 23 + (-25) + (-23)
= [15 + (-25)] + [23 + (-23)]
= (-10) + 0 = -10
d) 60 + 33 + (-50) + (-33)
= [60 + (-50)] + [33 + (-33)]
= 10 + 0 = 10
e) (-16) + (-209) + (-14) + 209
= [(-16) + (-14)] + [(-209) + 209]
= (-30) + 0 = -30
f) \(-3^2+\left(-54\right)\div\left[\left(-2\right)^8+7\right]\times\left(-2\right)^2\\ =\left(-9\right)+\left(-54\right)\div263\times4\\ =\left(-9\right)+\dfrac{-216}{263}=\dfrac{-2583}{263}\)
a. \(\left[\left(-37\right)+37\right]+\left(14+16\right)\) = 30
B. \(\left[\left(-24\right)+24\right]+\left(10+6\right)\) = 16
C. \(\left[\left(-23\right)+23\right]+\left(15-23\right)\)= -8
d. \(\left[33-33\right]+\left(60-50\right)\) = 10
e. \(\left(209-209\right)+\left(-16-14\right)\)= -30
a, (-17) + 21 + 79 + 17
= (-17 + 17) + (21 + 79)
= 0 + 100
= 100
b, 40 + 22 + (-16) + (-44)
= 40 + {(-16) + (-44} + 22
= 40 - 60 + 22
= - 20 + 22
= 2
c, (-12) + (-47) + (-28) + 47
= - (12 + 28) + (-47 + 47)
= - 40 + 0
= - 40
d, (- 5) + (-3) + 35 + (-17)
= (-5 + 35) - (3 + 17)
= 30 - 20
= 10
1. Tính tổng:
a) (-37) + 14 + 26 + 37 = 40
b) (-24) + 6 + 10 + 24 = 16
c) 15 + 23 + (-25) + (-23) = -10
d) 60 + 33 + (-50) + (-33) = 10
e) (-16) + (-209) + (-14) + 209 = -30
f) -32 + {-54 : [(-2)8 + 7] . (-2)2} = -32 + {-54 : [(-256) + 7] . 4} = -32 + {-54 : (-249) . 4} = -32 + {-54 : (-996)} = -32 + 0 = -32
2. Thực hiện phép tính:
a) (36 + 79) + (145 - 79 - 36) = 115 + 30 = 145
b) 10 - [12 - (-9 - 1)] = 10 - [12 - (-10)] = 10 - [12 + 10] = 10 - 22 = -12
c) (38 - 29 + 43) - (43 + 38) = 52 - 81 = -29
d) 271 - [(-43) + 271 - (-17)] = 271 - [-43 + 271 + 17] = 271 - [245] = 26
3. Tính hợp lý:
a) 31 . (-18) + 31 . (-81) - 31 = -558 + (-2511) - 31 = -3100
b) (-12) . 47 + (-12) . 52 + (-12) = -564 + (-624) + (-12) = -1200
c) 13 . (23 + 22) - 3 . (17 + 28) = 13 . 45 - 3 . 45 = 585 - 135 = 450
d) -48 + 48 . (-78) + 48 . (-21) = -48 + (-3744) + (-1008) = -4800
1. Tính tổng:
a) (-37) + 14 + 26 + 37 = 40
b) (-24) + 6 + 10 + 24 = 16
c) 15 + 23 + (-25) + (-23) = -10
d) 60 + 33 + (-50) + (-33) = 10
e) (-16) + (-209) + (-14) + 209 = -30
f) -32 + {-54 : [(-2)8 + 7] . (-2)2} = -32 + {-54 : [(-256) + 7] . 4} = -32 + {-54 : (-249) . 4} = -32 + {-54 : (-996)} = -32 + 0 = -32
2. Thực hiện phép tính:
a) (36 + 79) + (145 - 79 - 36) = 115 + 30 = 145
b) 10 - [12 - (-9 - 1)] = 10 - [12 - (-10)] = 10 - [12 + 10] = 10 - 22 = -12
c) (38 - 29 + 43) - (43 + 38) = 52 - 81 = -29
d) 271 - [(-43) + 271 - (-17)] = 271 - [-43 + 271 + 17] = 271 - [245] = 26
3. Tính hợp lý:
a) 31 . (-18) + 31 . (-81) - 31 = -558 + (-2511) - 31 = -3100
b) (-12) . 47 + (-12) . 52 + (-12) = -564 + (-624) + (-12) = -1200
c) 13 . (23 + 22) - 3 . (17 + 28) = 13 . 45 - 3 . 45 = 585 - 135 = 450
d) -48 + 48 . (-78) + 48 . (-21) = -48 + (-3744) + (-1008) = -4800
A=\(2^2-9^3+4^{-2}.16-2.5^2\)
\(=4-729+1-50=-774\)
B=\(\left(2^3.2\right).\dfrac{1}{2}+3^{-2}.3^2-7.1+5\)
\(B=2^4.\dfrac{1}{2}+1-7+5=8+1-7+5=7\)
C = 2-3 + (52)3.5-3 + 4-3.16 - 2.32 - 105.(\(\dfrac{24}{51}\))0
C = \(\dfrac{1}{8}\) + 56.5-3 + 4-3.42 - 2.9 - 105.1
C = \(\dfrac{1}{8}\) + 53 + \(\dfrac{1}{4}\) - 18 - 105
C = (\(\dfrac{1}{8}\) + \(\dfrac{1}{4}\)) - (105 - 125 + 18)
C = \(\dfrac{3}{8}\) - (-20 + 18)
C = \(\dfrac{3}{8}\) + 2
C = \(\dfrac{19}{8}\)
Ta có :
a) \(5^9:5^7+2^4.3-29.2012^0\)
\(=5^2+16.3-29.1\)
\(=25+48-29=44\)
b) \(\left[32+\left(-17\right)+\left(-15\right)+\left(-34\right)\right]+\left(-\left|-56\right|\right)\)
\(=\left[34-2-17-15-34\right]+\left(-56\right)\)
\(=\left[0-2-17-15\right]-56\)
\(=-34-56=-90\)
a) \(=\left(\left(-\frac{1}{4}-\frac{5}{3}\right)+\frac{7}{33}\right)-\left(-\frac{15}{12}+\frac{6}{11}-\frac{48}{49}\right)\)
\(=\left(-\frac{23}{12}+\frac{7}{33}\right)+\frac{15}{12}-\frac{6}{11}+\frac{48}{49}\)
\(=\left(-\frac{23}{12}+\frac{15}{12}\right)+\left(\frac{9}{33}-\frac{6}{11}\right)+\frac{48}{49}\)
\(=-\frac{2}{3}-\frac{3}{11}+\frac{48}{49}\)
\(=\frac{65}{1617}\)
b) \(=\frac{11}{125}+\left(-\frac{17}{18}+\frac{4}{9}\right)+\left(-\frac{5}{7}+\frac{17}{14}\right)\)
\(=\frac{11}{125}-\frac{1}{2}+\frac{1}{2}\)
\(=\frac{11}{125}\)
\(\frac{3}{2}+\frac{5}{4}+\frac{9}{8}+\frac{17}{16}+\frac{33}{32}+\)\(\frac{65}{64}-7\)
\(=\frac{96}{64}+\frac{80}{64}+\frac{72}{64}+\frac{66}{64}+\frac{65}{64}-7\)
\(=\frac{96+80+72+66+64}{64}-7\)
\(=\frac{378}{64}-\frac{7}{1}\)
\(=\frac{189}{32}-\frac{224}{32}\)
\(=\frac{-35}{32}\)