Câu 1:
Đặt \(A=1.2+2.3+3.4+99.100\)
\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100\left(101-98\right)\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)
\(\Rightarrow3A=99.100.101\)
\(\Rightarrow A=99.100.101:3\)
\(\Rightarrow A=33.100.101\)
\(\Rightarrow A=333300\)
Vậy A = 333300
Câu 2:
\(\left(2x-1\right)^4=81\)
\(\Rightarrow2x-1=\pm3\)
+) \(2x-1=3\Rightarrow x=2\)
+) \(2x-1=-3\Rightarrow x=-1\)
Vậy \(x\in\left\{2;-1\right\}\)
Câu 3:
C1: Giải:
Ta có: \(\frac{b}{a}=\frac{d}{c}\Rightarrow\frac{a}{b}=\frac{c}{d}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}=\frac{a-c}{b-d}\)
\(\Rightarrow\frac{a+c}{b+d}=\frac{a-c}{b-d}\)
\(\Rightarrow\frac{a+c}{a-c}=\frac{b+d}{b-d}\left(đpcm\right)\)
C2: Đặt = k
