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\(\text{Có 3 trường hợp có thể xảy ra:}\)
\(A=B\)
\(A< B\)
\(A>B\)
Bài 1:
a) 8154-(674+8154)+(-98+674)
=8154-674-8154-98+674
=-98
b) -25-21+25-72+49*25
=-21-72+1225
=1132
c) \(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{3}-\frac{1}{10}=\frac{7}{30}\)
Bài 2)
a) \(A=\left(-a+b-c\right)-\left(-a-b-c\right)\)
\(=-a+b-c+a+b+c=2b\)
b) \(B=\left(2a+b\right)-3b+\left(a-3c\right)-\left(3a+2c\right)\)
\(=2a+b-3b+a-3c-3a-2c=-2b-5c\)
1. Tính nhanh
a) 8154 - (674 + 8154) + (-98+674)
= 8154 - 674 - 8154 - 98 + 674
= (8154 - 8154) + (674 - 674) - 98
= 0 + 0 - 98
= -98
b) -25 - 21 + 25 - 72 + 49 . 25
= [(-25) + 25] - 21 - 72 + 49 . 25
= 0 - 21 - 72 + 49 . 25
= (-21 - 72) + (49 . 25)
= -93 + 1225
= 1132
c) \(\frac{1}{3.4}\) + \(\frac{1}{4.5}\) + \(\frac{1}{5.6}\) + \(\frac{1}{6.7}\) + \(\frac{1}{7.8}\) + \(\frac{1}{8.9}\) + \(\frac{1}{9.10}\)
= \(\frac{1}{3}-\frac{1}{4}\) + \(\frac{1}{4}-\frac{1}{5}\) + \(\frac{1}{5}-\frac{1}{6}\) + \(\frac{1}{6}-\frac{1}{7}\) + \(\frac{1}{7}-\frac{1}{8}\) + \(\frac{1}{8}-\frac{1}{9}\)+ \(\frac{1}{9}-\frac{1}{10}\)
= \(\frac{1}{3}-\frac{1}{10}\)
= \(\frac{7}{30}\)
2. Bỏ dấu ngoặc, thu gọn biểu thức
a) A = (-a + b - c) - (-a - b - c)
A = (-a) + b - c + a + b + c
A = (-a + a) + (b + b) + (c - c)
A = 0 + 2b + 0
A = 2b
b) B = (2a + b - 3b) + (a - 3c) - (3a + 2c)
B = 2a + b - 3b + a - 3c - 3a - 2c
B = (2a + a - 3a) + (b - 3b) + (-3c - 2c)
B = a(2 + 1 - 3) + b(1 - 3) + c(-3 - 2)
B = a0 + b . (-2) + c . (-5)
B = 0 + b . (-2) + c . (-5)
B = b . (-2) + c . (-5)
a) Ta có: A = 1.2 + 2.3 + 3.4 + 4.5 +....+ 98.99
\(\Rightarrow\) 3A = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 +....+ 98.99.3
\(\Rightarrow\) 3A = 1.2.3 + 2.3(4-1) + 3.4(5-2) + 4.5(6-3) +.....+ 98.99(100-97)
\(\Rightarrow\) 3A = 1.2.3 + 2.3.4 - 2.3.1 + 3.4.5 - 3.4.2 + 4.5.6 - 4.5.3 + ....+ 98.99.100 - 98.99.97
\(\Rightarrow\) 3A = 98.99.100
\(\Rightarrow\) A = \(\frac{98.99.100}{3}\) = 323400
Vậy A = 323400
b) Ta có: B = 12 + 22 + 32 +......+ 982
\(\Rightarrow\) B = 1.1 + 2.2 + 3.3 + .....+ 98.98
\(\Rightarrow\) B = 1(2-1) + 2(3-1) + 3(4-1) + .......+ 98(99-1)
\(\Rightarrow\) B = 1.2 - 1 + 2.3 - 2 + 3.4 - 3 +......+ 98.99 -98
\(\Rightarrow\) B = (1.2 + 2.3 + 3.4 +........+ 98.99) - (1 + 2 + 3 +.....+ 98)
\(\Rightarrow\) B = (1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 +....+ 98.99.3) : 3 - 4851
\(\Rightarrow\) B = [1.2.3 + 2.3(4-1) + 3.4(5-2) + 4.5(6-3) +.....+ 98.99(100-97)] : 3 - 4851
\(\Rightarrow\) B = (1.2.3 + 2.3.4 - 2.3.1 + 3.4.5 - 3.4.2 + 4.5.6 - 4.5.3 + ....+ 98.99.100 - 98.99.97) : 3 + 4851
\(\Rightarrow\) B = \(\frac{\text{ 98.99.100 }}{3}\) + 4851
\(\Rightarrow\) B = 323400 + 4851
\(\Rightarrow\) B = 328251
Vậy B = 328251
Ta có: A = 1.2 + 2.3 + 3.4 + 4.5 +....+ 98.99
⇒⇒ 3A = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 +....+ 98.99.3
⇒⇒ 3A = 1.2.3 + 2.3(4-1) + 3.4(5-2) + 4.5(6-3) +.....+ 98.99(100-97)
⇒⇒ 3A = 1.2.3 + 2.3.4 - 2.3.1 + 3.4.5 - 3.4.2 + 4.5.6 - 4.5.3 + ....+ 98.99.100 - 98.99.97
⇒⇒ 3A = 98.99.100
⇒⇒ A = 98.99.100398.99.1003 = 323400
b, tự giải nhé
Cho A=1/1.2 + 1/2.3 + + 1/ 3.4+...+1/49.50 ; B = 1.2+2.3+3.4+4.5+5.6+...+49.50
Tính 50 mủ 2 A – B/17
Vì
\(\frac{1}{2}< \frac{2}{3};\frac{3}{4}< \frac{4}{5};\frac{5}{6}< \frac{6}{7};...;\frac{99}{100}< \frac{100}{101}\)
\(\Rightarrow\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}< \frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\)
\(\Rightarrow a< b\)
\(3A=3.4.3+4.5.3+5.6.3+...+59.60.3\)
\(3A=3.4\left(5-2\right)+4.5\left(6-3\right)+5.6.\left(7-4\right)+...+59.60\left(61-58\right)\)
\(3A=3.4.5-2.3.4+4.5.6-3.4.5+...+59.60.61-58.59.60\)
\(3A=59.60.61-2.3.4\)
\(\Rightarrow A=59.20.61-2.4=...\)