\(\Leftrightarrow\left(\dfrac{x-1}{99}-1\right)+\left(\dfrac{x-99}{1}-1\right)+\left(\dfrac{x-3}{97}-1\right)+\left(\dfrac{x-97}{3}-1\right)+\left(\dfrac{x-5}{95}-1\right)+\left(\dfrac{x-95}{5}-1\right)=0\)

=>x-100=0

=>x=100

\(\text{1: 1+(-2)+3+(-4)+........+19+(-20)}\)

\(\text{=1-2+3-4+.....+19-20}\)

\(\text{=-1+(-1)+..........+(-1)}\)

\(\text{=-1.(20-1)+1:2}\)

\(\text{=-1.10}\)

\(=-10\)

\(\text{2: 1- 2 +3 -4+......+99 - 100}\)

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

\(\text{=-1+(-1)+.....+(-1)}\)

\(\text{=-1.(100-1)+1:2}\\ \text{=-1.50}\)

\(=-50\)

\(\text{3: 2 - 4+6 - 8+.....+48 - 50}\\ \text{=(2 - 4)+(6 - 8)+.....+(48 - 50)}\\ \text{=-2+(-2)+......+(-2)}\\ \text{=-2.(50-2):2+1}\\ \text{=-2.25}\\ =-50\)

\(\text{4: -1 + 3 - 5 +7 -.....+97 - 99}\\ \text{=-1 +(3-5)+(7-9)+.......+(97-99)}\\ \text{=-1+(-2)+(-2)+........+(-2)}\\ \text{=-1+[(-2).(99-3):2+1]}\\ \text{=-1+[(-2).49]}\\ \text{=-1+(-98)}\\ =-99\)

\(\text{5: 1 + 2 – 3 – 4 + . . . . + 97 + 98 – 99 – 100}\)

\(\text{=1−2+3−4+5−6+...+99−100}\)

\(\text{=(1−2)+(3−4)+(5−6)+...+(99−100) }\)

\(\text{=(−1)+(−1)+(−1)+...+(−1)}\)

\(\text{=(−1).50}\)

\(\text{=−50}\)

1/ 1 + (-2) + 3 + (-4) + . . . + 19 + (-20)

=(1-2)+(3-4)+..........+(19-20)

=-1+(-1)+.......+(-1)

=-1.[(20-1)+1:2]

=-1.10

=-10

2/ 1 – 2 + 3 – 4 + . . . + 99 – 100

=-1+(-1)+....+(-1)

=-1.[(100-1)+1:2]

=-1.50

=-50

3/ 2 – 4 + 6 – 8 + . . . + 48 – 50

=-2+(-2)+.......+(-2)

=-2.[(50-2):2]:2

=-2.12

=-24

=-2.

a) A = 2 + 4 + 6 + 8 + ... + 1000

Ta có : A = 2 + 4 + 6 + 8 + ... + 1000 ( có 500 số )

               = (1000 + 2) . 500 : 2 = 250500

c) \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}+\frac{2}{99.101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}=\frac{100}{101}\)

kinh q u e