Bài 1
Ta thấy: \(\left|x+4\right|\ge0\forall x\)
\(\Rightarrow B=\left|x+4\right|+1996\ge1996\forall x\)
Đẳng thức xảy ra khi \(\left|x+4\right|=0\Leftrightarrow x=-4\)
Vậy \(B_{Min}=1996\) khi \(x=-4\)
Bài 2
\(S=\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{49\cdot50}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\)
\(=\dfrac{1}{2}-\dfrac{1}{50}=\dfrac{12}{25}\)
Bài 3
\(S=1+5^2+5^4+5^6+...+5^{2020}\)
\(5^2S=5^2\left(1+5^2+5^4+5^6+...+5^{2020}\right)\)
\(25S=5^2+5^4+5^6+....+5^{2022}\)
\(25S-S=\left(5^2+5^4+...+5^{2022}\right)-\left(1+5^2+...+5^{2020}\right)\)
\(24S=5^{2022}-1\Rightarrow S=\dfrac{5^{2022}-1}{24}\)
