\(B=\left[1+\left(-3\right)\right]+\left[5+\left(-7\right)\right]+........+\left[97+\left(-99\right)\right]+101\)

\(=\left(-2\right)+\left(-2\right)+.......+\left(-2\right)+101\)( có 25 số -2)

\(=\left(-2\right).25+101\)

\(=\left(-50\right)+101\)

\(=51\)

\(B=1+\left(-3\right)+5+\left(-7\right)+...+97+\left(-99\right)+101\)

\(\Rightarrow B=\left[1+\left(-3\right)\right]+\left[5+\left(-7\right)\right]+...+\left[97+\left(-99\right)\right]+101\)

\(\Rightarrow B=\left(-2\right)+\left(-2\right)+...+\left(-2\right)+101\)

                     có 25 số -2

\(\Rightarrow B=\left(-2\right).25+101\)

\(\Rightarrow B=-50+101\)

\(\Rightarrow B=51\)

Trả lời:

\(B=1+\left(-3\right)+5+\left(-7\right)+...+97+\left(-99\right)+101\)(Có 51 số)

\(B=\left[1+\left(-3\right)\right]+\left[5+\left(-7\right)\right]+...+\left[97+\left(-99\right)\right]+101\)

\(B=\left(-2\right)+\left(-2\right)+...+\left(-2\right)+101\)( Có 25 số (-2) )

\(B=\left(-2\right)\times25+101\)

\(B=\left(-50\right)+101\)

\(B=51\)

Vậy\(B=51\)

Hok tốt!

Good girl

a) (–38) + 28 = –(38 – 28) = –10.

b) 273 + (–123) = 273 – 123 = 150.

c) 99 + (–100) + 101 = (99 + 101) + (–100) = 200 + (–100) = 100.

\(A=\dfrac{99}{100}\cdot\dfrac{98}{99}\cdot...\cdot\dfrac{1}{2}=\dfrac{1}{100}\)

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\)

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

\(=1-\dfrac{1}{100}=\dfrac{99}{100}\)

b, \(\left(1-\dfrac{1}{100}\right)\left(1-\dfrac{1}{99}\right)...\left(1-\dfrac{1}{2}\right)=\dfrac{99.98...1}{100.99...2}=\dfrac{1}{100}\)

Lời giải:

a. $(-2018)+2018=2018-2018=0$

b) $57+(-93)=-(93-57)=-36$

c) $(-38)+46=46-38=8$

Tính: 

a) 

b) 

c) 

a) (- 2018) + 2018 = - (2018 – 2018) = 0

b) 57 + (- 93) = (93 – 57) = 38

c) (- 38) + 46 = - (38 – 48) = 8

\(a,\left(\frac{2}{5}\right)^6.\left(\frac{25}{4}\right)^2=\left(\frac{2}{2.3}\right)^6.\left(\frac{5}{2}\right)^4\)

\(=\frac{1}{3^6}.\frac{5^4}{2^4}=\frac{5^4}{3^6.2^4}\)

\(b,\frac{100}{123}:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)\)

\(=\frac{100}{123}:\left(\frac{9+7}{12}\right)+\frac{23}{123}:\left(\frac{27-7}{15}\right)\)

\(=\frac{100}{123}:\frac{16}{12}+\frac{23}{123}:\frac{20}{15}\)

\(=\frac{100.12}{123.16}+\frac{23.15}{123.20}\)

\(=\frac{5.5.4.3.4}{41.3.4.4}+\frac{23.3.5}{41.3.4.5}\)

\(=\frac{25}{41}+\frac{23}{164}=\frac{25.4+23}{164}\)

\(=\frac{123}{164}=\frac{3}{4}\)

=> ĐK:  \(x\ne\left\{0;-1;-2;...;-99;-100\right\}\)

Đây là dạng dãy số đặc biệt, bạn có thể giải như sau:

Ta có:

\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+...+\frac{1}{\left(x+99\right)\left(x+100\right)}=\frac{100}{101}\)

\(\Leftrightarrow\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+2}+...+\frac{1}{x+99}-\frac{1}{x+100}=\frac{100}{101}\)

\(\Leftrightarrow\frac{1}{x}-\frac{1}{x+100}=\frac{100}{101}\)

\(\Leftrightarrow\frac{x+100-x}{x.\left(x+100\right)}=\frac{100}{101}\)

\(\Leftrightarrow\frac{100}{x^2+100x}=\frac{100}{101}\)

\(\Leftrightarrow x^2+100x=101\)

\(\Leftrightarrow x^2+100x-101=0\)

\(\Leftrightarrow x^2+101x-x-101=0\)

\(\Leftrightarrow x\left(x+101\right)-\left(x+101\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+101\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x+101=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1\left(n\right)\\x=-101\left(n\right)\end{cases}}\)

Vậy: S={1;-101)