=(-1+2)-(3+4)-(5+6)-........-(2017+2018)

=1-7-11-........-4035

=-1009

a) \(\left(x-5\right)^{12}=\left(x-5\right)^{10}\)

\(\Rightarrow\left(x-5\right)^{12}-\left(x-5\right)^{10}=0\)

\(\Rightarrow\left(x-5\right)^{10}\left[\left(x-5\right)^2-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)^{10}=0\\\left(x-5\right)^2-1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)^{10}=0^{10}\\\left(x-5\right)^2=0+1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x-5=0\\\left(x-5\right)^2=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=0+5\\\left(x-5\right)^2=1^2\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=5\\x-5=\pm1\end{cases}}\)

\(\Rightarrow x=5;\orbr{\begin{cases}x-5=1\\x-5=-1\end{cases}}\)

\(\Rightarrow x=5;\orbr{\begin{cases}x=1+5\\x=-1+5\end{cases}}\)

\(\Rightarrow x=5;\orbr{\begin{cases}x=4\\x=6\end{cases}}\)

Vậy x = 4 hoặc x = 5 hoặc x = 6 

\(a)\left(x-5\right)^{12}=\left(x-5\right)^{10}\)

\(\Leftrightarrow\left(x-5\right)^{12}-\left(x-5\right)^{10}=0\)

\(\Leftrightarrow\left(x-5\right)^{10}\left[\left(x-5\right)^2-1\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}\left(x-5\right)^{10}=0\\\left(x-5\right)^2-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x-5=0\\\left(x-4\right)\left(x-6\right)=0\end{cases}}\)

[  ra \(\left(x-4\right)\left(x-6\right)\)do \(\left(x-5\right)^2-1=\left(x-5-1\right)\left(x-5+1\right)=\left(x-6\right)\left(x-4\right)\)]

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=4;x=6\end{cases}}\)

_Minh ngụy_

Câu b thiếu '= ......"

\(\(c)\frac{1}{2.4}+\frac{1}{4.6}+.....+\frac{1}{2x\left(2x+2\right)}=\frac{3}{16}\)\)

\(\(\Rightarrow\frac{1}{4.\left(1.2\right)}+\frac{1}{4.\left(2.3\right)}+......+\frac{1}{4\left(x-1\right).x}=\frac{3}{16}\)\)

\(\(\Leftrightarrow\frac{1}{4}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{2.3}+....+\frac{1}{x\left(x-1\right)}\right)=\frac{3}{16}\)\)

\(\(\Rightarrow\frac{2-1}{1.2}+\frac{3-2}{2.3}+.......+\frac{x-\left(x-1\right)}{x\left(x-1\right)}=\frac{3}{4}\)\)

\(\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-........+\frac{1}{x-1}-\frac{1}{x}=\frac{3}{4}\)\)

\(\(\Leftrightarrow1-\frac{1}{x}=\frac{3}{4}\)\)

\(\(\Leftrightarrow\frac{1}{x}=\frac{1}{4}\)\)

\(\(\Rightarrow x=4\left(t/m:x\ne0\right)\)\)

_Minh ngụy_

Ta có:

B=1/2-1/2^2-1/2^3-...-1/2^100

B/2=1/2^2-1/2^3-1/2^4-....-1/2^101

B/2-B=1/2^101-1/2

=>B=(1/2^101-1/2).2

Vậy:B=(1/2^101-1/2).2

Bạn nào làm đc nhanh mình sẽ k

Bạn làm nhanh và đúng nhất mình sẽ k

\(a,\dfrac{3}{5}+\dfrac{3}{5\cdot9}+\dfrac{3}{9\cdot13}+....+\dfrac{3}{97\cdot101}\)

\(=\dfrac{3}{4}\cdot\left(\dfrac{4}{5}+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+....+\dfrac{4}{97\cdot101}\right)\)

\(=\dfrac{3}{4}\cdot\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+....+\dfrac{1}{97}-\dfrac{1}{101}\right)\)

\(=\dfrac{3}{4}\cdot\left(1-\dfrac{1}{101}\right)\)

\(=\dfrac{3}{4}\cdot\dfrac{100}{101}\)

\(=\dfrac{75}{101}\)

\(b,\left(1+\dfrac{1}{2}\right)\cdot\left(1+\dfrac{1}{3}\right)\cdot\left(1+\dfrac{1}{4}\right)\cdot....\cdot\left(1+\dfrac{1}{99}\right)\)

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

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

Tính nhanh:

a) \(\dfrac{3}{5}+\dfrac{3}{5.9}+\dfrac{3}{9.13}+...+\dfrac{3}{97.101}\)

= \(\dfrac{3}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{101}\right)\)

= \(\dfrac{3}{4}\left(1-\dfrac{1}{101}\right)\)

= \(\dfrac{3}{4}\times\dfrac{100}{101}\)

= \(\dfrac{75}{101}\)

b) \(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)...\left(\dfrac{1}{98}+1\right)\left(\dfrac{1}{99}+1\right)\)

\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}...\dfrac{99}{98}.\dfrac{100}{99}\)

\(=\dfrac{3.4.5...99.100}{2.3.4...98.99}\)

\(=\dfrac{100}{2}\)

\(=50\)

a) Các số có dạng : \(\frac{1}{a\left(a+1\right)}=\frac{\left(a+1\right)-a}{a\left(a+1\right)}=\frac{1}{a}-\)\(\frac{1}{a+1}\)

Thế vào bởi các số sẽ có kết quả

b) Các số có dạng : \(\frac{1}{a\left(a+2\right)}=\frac{1}{2}.\frac{2}{a\left(a+2\right)}=\frac{1}{2}.\frac{\left(a+2\right)-a}{a\left(a+2\right)}\)\(=\frac{1}{2}.\left(\frac{1}{a}-\frac{1}{a+2}\right)\)

Làm tương tự trên

c) Lấy nhân tử chung là 5 rồi làm như câu a)

bạn có thể làm ra hộ mình được ko mình ko hiểu

a là j vậy