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1/1 x 2 + 1/2x 3 + 1/3 x 4 + ... + 1/99 x 100 

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/99 - 1/100

= 1 - 1/100

= 100/100 - 1/100

=  99/100 

Chúc học giỏi !!! TK mình nha !! 

1/2346

\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right)\)

\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{100}{99}\)

\(=\frac{100}{2}=50\)

Thanks nhìu

phương trình này nhìn từ đầu cũng bik vô nghiệm ko có x

\(\frac{x+1}{99}+\frac{x+2}{99}=\frac{x+10}{99}+\frac{x+20}{99}\)

Nhân 2 vế cho 99 ta được:

\(99.\left(\frac{x+1}{99}+\frac{x+2}{99}\right)=99.\left(\frac{x+10}{99}+\frac{x+20}{99}\right)\)

=>x+1+x+2=x+10+x+20

=>2x+3=2x+30

=>0x=27 (vô lí)

Vậy ko tìm dc x

(x+1)+(x+2)+(x+3)+.......+(x+99)+(x+100)=5750

(x+x+x+...+x)+(1+2+3+...+100) = 5750

100x+5050 = 5750

100x = 5750-5050

100x = 700

x = 700 : 100

x = 7

 \(\left(-1\right)\cdot\left(-1\right)^2\cdot\left(-1\right)^3\cdot...\cdot\left(-1\right)^{98}\cdot\left(-1\right)^{99}\)

\(=\left(-1\right)\cdot1\cdot\left(-1\right)\cdot...\cdot1\cdot\left(-1\right)\)

\(=\left(-1\cdot-1\cdot...\cdot-1\right)\cdot\left(1\cdot1\cdot...\cdot1\right)\)

\(=1\cdot1\)

\(=1\)

k mình

k lại

\(99\times36+57\times99+99-84\times99\)

\(=99\times(36+57+1-84)\)

\(=99\times10=990\)

99 x 36 + 57 x 99 - 84 x 99

= 99 x ( 36 + 57 + 1 - 84 )

= 99 x 10

= 990

99 x 36 + 57 x 99 + 99 - 84 x 99

= 99 x ( 36 + 57 + 99 - 84 )

= 99 x 108

= 10.692