=-20 mai zo mai zo tick ug ho đi

-20

**** mình nha

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(A=1-\frac{1}{100}\)

\(A=\frac{99}{100}\)

\(B=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)

\(B=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{107}-\frac{1}{111}\)

\(B=\frac{1}{3}-\frac{1}{111}\)

\(B=\frac{12}{37}\)

\(C=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

\(C=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(C=7\left(\frac{1}{10}-\frac{1}{70}\right)\)

\(C=7.\frac{3}{35}\)

\(C=\frac{3}{5}\)

Ta có:

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(A=\frac{1}{1}-\frac{1}{100}=\frac{99}{100}\)

\(B=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)

\(B=4.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\right)\)

\(B=4.\left(\frac{1}{3}-\frac{1}{111}\right)=4.\frac{12}{37}=\frac{48}{37}\)

\(C=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

\(C=7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)

\(C=7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}=\frac{3}{5}\)

-Quy luật: Nhân mỗi vế của đẳng thức cho số thích hợp để tạo ra đẳng thức mới, khi cộng (hoặc trừ) mỗi vế của mỗi đẳng thức thì sẽ rút gọn bớt.

a) \(A=2-2^2+2^3-2^4+...+2^{99}-2^{100}\)

\(\Rightarrow2A=2^2-2^3+2^4-2^5+...+2^{100}-2^{101}\)

\(\Rightarrow2A+A=2^2-2^3+2^4-2^5+...+2^{100}-2^{101}+\left(2-2^2+2^3-2^4+...+2^{99}-2^{100}\right)\)

\(\Rightarrow A=-2^{101}+2\)

b,c) làm tương tự. 

d) \(D=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{100}}\)

\(\Rightarrow3D=3+1+\dfrac{1}{3}+...+\dfrac{1}{3^{99}}\)

\(\Rightarrow3D-D=3+1+\dfrac{1}{3}+...+\dfrac{1}{3^{99}}-\left(1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{100}}\right)\)

\(\Rightarrow2D=3+\dfrac{1}{3^{100}}\)

\(\Rightarrow2D=\dfrac{3^{101}+1}{3^{100}}\Rightarrow D=\dfrac{3^{101}+1}{2.3^{100}}\)

e) làm tương tự nhưng đổi thành cộng.

89 156 .<.. 98 516           69 731 ..>. 69 713

79 650 .=.. 79 650              67 628 .<.. 67 728

89 156 < 98 516 69 731 = 69 731

79 650 = 79 650 67 628 < 67 728

Chắc minh ko nhớ nỗi đâu nhưq hay vẫn pải khen ^^

Bài 1: 

b: 27-(5-|x|)=31

=>5-|x|=-4

=>|x|=9

=>x=9 hoặc x=-9

c: -13-(6-|x+1|)=24

=>6-|x+1|=-37

=>|x+1|=43

=>x+1=43 hoặc x+1=-43

=>x=42 hoặc x=-44

a, 100 + 98 + 96 + ... + 2 - 9 7 - 95 - .. -1

=  100 + (98 - 97) + (96-95) + ... +  + ... + (2 - 1)

= 100 + 1 + 1 + 1 +.. +1

= 100 + 1 x49

= 100 + 49 

= 149

b , 1 + 2 - 3 - 4 + 5 + 6 - .... -299 - 330 +301 + 302 

 =( 1 + 2 - 3) + ( -4 + 5 + 6 -7 )  +... +(298 - 299 -300 +301 ) + 302

= 0 + 0 + .. + 0 + 302

= 302 

c)  2 . 31 . 12 + 4 . 6 . 42 + 8 . 27 . 3

=24.31+24.42+24.27

=24.(31+42+27)

=24.100

=2400

d)

=36x(28+82)+64x(69+41)

=36x110+64x110

=110x(26+64)

=110x100

=11000

d) dãy tính trên có số số tự nhiên là: (99-1):2+1=50(số)

99-97+95-93+91-89+...+7-5+3-1(50:2=25 cặp)

(99-97)+(95-93)+(91-89)+...+(7-5)+(3-1) (25 cặp)

2+2+2+2+2+...+2+2(25 số 2)

2x25=50

1. (-34)+24+(-7)+27=-10+20=10

2.99+(-100)+101=(99+101)+(-100)=200-100=100

3.(-75)+69+(-25)+131=(69+131)-(75+25)=200-100=100

1) \(\left(-34\right)+24+\left(-7\right)+27\)

\(=-34+24-7+27\)

\(=-\left(34-24\right)-7+27\)

\(=-10-7+27\)

\(=-\left(10+7\right)+27\)

\(=-17+27\)

\(=27-17\)

\(=10\)

2) \(99+\left(-100\right)+101\)

\(=99-100+101\)

\(=-100+99+101\)

\(=-\left(100-99\right)+101\)

\(=-1+101\)

\(=101-1\)

\(=100\)

3) \(\left(-75\right)+69+\left(-25\right)+131\)

\(=-75+69-25+131\)

\(=-\left(75-69\right)-25+131\)

\(=-6-25+131\)

\(=-\left(6+25\right)+131\)

\(=-31+131\)

\(=131-31\)

\(=100\)