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\(\left(-6\right).3+6.\left(-11\right)+\left(-6\right).\left(-2\right)\)
\(=\left(-6\right).3+\left(-6\right).11+\left(-6\right).\left(-2\right)\)
\(=\left(-6\right).\left[3+11+\left(-2\right)\right]\)
\(=\left(-6\right).12\)
\(=-72\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{100}{100}-\frac{1}{100}\)
\(=\frac{99}{100}\)
\(\frac{\left(3.4.2^4\right)^2}{5.2^5.4^2-16^2}\)
\(=\frac{\left(3.2^2.2^4\right)^2}{5.2^5\left(2^2\right)^2-\left(2^4\right)^2}\)
\(=\frac{\left(3.2^6\right)^2}{5.2^9-2^8}\)
\(=\frac{3^2.2^{12}}{2^8\left(5.2-1\right)}\)
\(=\frac{9.2^4}{9}\)
\(=16\)
\(\dfrac{1}{2}A=\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+\left(\dfrac{1}{2}\right)^4+...+\left(\dfrac{1}{2}\right)^{2023}\)
\(A-\dfrac{1}{2}A=\left(\dfrac{1}{2}\right)^{2023}-1\)
\(\dfrac{1}{2}A=\left(\dfrac{1}{2}\right)^{2023}-1\)
\(A=\dfrac{1}{2^{2022}}-2\)
12A=12+(12)2+(12)3+(12)4+...+(12)202312A=12+(12)2+(12)3+(12)4+...+(12)2023
A−12A=(12)2023−1A−12A=(12)2023−1
12A=(12)2023−112A=(12)2023−1
A=122022−2