làm ơn hãy giúp mình

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{x\left(x+1\right)}=\frac{99}{100}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{x}-\frac{1}{x+1}=\frac{99}{100}\)

\(1-\frac{1}{x+1}=\frac{99}{100}\)

=> \(\frac{1}{x+1}=1-\frac{99}{100}=\frac{1}{100}\)

=> x+1 = 100

=> x = 100 - 1 

=> x = 99

mơ đi Nguyễn Đình Dũng

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)

\(< =>\frac{128}{256}+\frac{64}{256}+\frac{32}{256}+\frac{16}{256}+\frac{8}{256}+\frac{4}{256}+\frac{2}{256}+\frac{1}{256}\)

\(< =>\frac{128+64+32+16+8+4+2+1}{256}\)

\(< =>\frac{255}{256}\)

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

\(< =>\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(< =>\frac{1}{1}-\frac{1}{100}\)

\(< =>\frac{99}{100}\)

\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{100}\right)\)

\(< =>\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{99}{100}\)

\(< =>\frac{1\cdot2\cdot3\cdot...\cdot99}{2\cdot3\cdot4\cdot...\cdot100}\)

\(< =>\frac{1}{100}\)

mk chuc ban hoc tot nhe :))

1.

c. \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}\)

\(=\frac{49}{50}\)

2. 

a. \(45-5\left(y+1\right)=10\)

\(\Rightarrow5\left(y+1\right)=35\)

\(\Rightarrow y+1=7\)

\(\Rightarrow y=6\)

b. \(y:2+y:2=15\)

\(\Rightarrow\frac{1}{2}y+\frac{1}{2}y=15\)

\(\Rightarrow y=15\)

Bài 1 :

\(a,12,5\times32\times8\)

\(=\left(12,5\times8\right)\times32\)

\(=100\times32\)

\(=3200\)

\(b,20,9+20,9\times99\)

\(=20,9\times\left(1+99\right)\)

\(=20,9\times100\)

\(=2090\)

\(c,\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{49.50}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}\)

\(=\frac{50}{50}-\frac{1}{50}\)

\(=\frac{49}{50}\)

Bài 2 :

\(a,45-5\times\left(y+1\right)=10\)

\(5\times\left(y+1\right)=45-10\)

\(5\times\left(y+1\right)=35\)

\(y+1=35\div5\)

\(y+1=7\)

\(y=7-1\)

\(y=6\)

\(b,y\div2+y\div2=15\)

\(y\times\frac{1}{2}+y\times\frac{1}{2}=15\)

\(2\times\left(y\times\frac{1}{2}\right)=15\)

\(y=15\)

Học tốt

1/1.2 +1/2.3 +1/3.4 +....+1/99.100

=1-1/2+1/2-1/3+1/3-14+.....+1/99-1/100

=1-1/100

=99/100

e ko cop đâu nhé e lớp 6 câu nay e làm đc ạ !

A=1²/1.2 .2²/2.3 .3²/3.4 .4²/4.5

=1/2. 2.2/2.3 .3.3/3.4 .4.4/4.5

=1/2.2/3.3.4.4./5

=1/5

M = 5 + 5³ + 5⁵ + ... + 5⁴⁷ + 5⁴⁹

5²M = 5²(5 + 5³ + 5⁵ + ... + 5⁴⁷ + 5⁴⁹)

25M = 5³ + 5⁵ + 5⁷ + ... + 5⁴⁹ + 5⁵¹

25M - M = ( 5³ + 5⁵ + 5⁷ + ... + 5⁴⁹ + 5⁵¹) - (5 + 5³ + 5⁵ + ... + 5⁴⁷ + 5⁴⁹)

24M = 5⁵¹ - 5

M = \(\frac{5^{51}-5}{24}\)

Còn mấy câu kia bạn biết ko?

bài 2 tìm x

a,106- ( x+ 7) =9

x+7 = 106 - 9

x+7 = 107

x= 107 - 7

x=100

b, 2 x ( x+ 4) + 5 =65

2 x (x+4) = 65 - 5

2 x (x+4) = 60

x+4 = 60:2

x+4= 30

x= 30 - 4

x=26

c, (16x x -32) x 45=0

16 x X - 32 = 0: 45

16 x X - 32 =0

16 x X = 0 + 32

16 x X = 32

X= 32:16

X=2

d, x+4 x x = 100 : 5

X + 4 x X = 20

(1+4) x X = 20

5 x X  = 20

X= 20:5

X=4

ủa bài 1 đâu =]]