CMR:
a, -x (-x)^2n = x^2n
b, (-x)^2n+1 = -x^2n+1
Giúp mk vs nha. Mk tik cho
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\(\Leftrightarrow5^3\times\left(-2\right)^3\times\left(-61\right)\times1\)\(1\)
\(=[5\times\left(-2\right)]^3\times\left(-61\right)\)
\(=\left(-10\right)^3\times\left(-61\right)\)
\(=\left(-1000\right)\times\left(-61\right)\)
\(=61000\)
\(D= \dfrac{1}{1.3} + \dfrac{1}{3.5}+...+\dfrac{1}{\left(2n-1\right).\left(2n+1\right)}\),
\(2.D = \dfrac{2}{1.3}+ \dfrac{2}{3.5}+...+\dfrac{2}{\left(2n-1\right).\left(2n+1\right)}\)
\(2.D = 1 - \dfrac{1}{3} + \dfrac{1}{3}- \dfrac{1}{5} +\dfrac{1}{5}- \dfrac{1}{7} + ... + \dfrac{1}{\left(2n-1\right)}-\dfrac{1}{\left(2n+1\right)}\)
\(2.D = 1 - \dfrac{1}{\left(2n+1\right)}\)
\(2.D= \dfrac{2n}{\left(2n+1\right)} \)
Vậy \(D = \dfrac{n}{\left(2n+1\right)}\)
\(E=\dfrac{1}{1.3.5}+\dfrac{1}{3.5.7}+\dfrac{1}{5.7.9}+...+\dfrac{1}{\left(2n-1\right).\left(2n+1\right).\left(2n+3\right)}\)
\(\Rightarrow4E=4.\dfrac{1}{1.3.5}+\dfrac{1}{3.5.7}+\dfrac{1}{5.7.9}+...+\dfrac{1}{\left(2n-1\right).\left(2n+1\right).\left(2n+3\right)}\)
\(=\dfrac{4}{1.3.5}+\dfrac{4}{3.5.7}+...+\dfrac{4}{\left(2n-1\right).\left(2n+1\right).\left(2n+3\right)}\)
\(=\dfrac{1}{1.3}-\dfrac{1}{3.5}+\dfrac{1}{3.5}-\dfrac{1}{5.7}-...+\dfrac{1}{\left(2n-1\right).\left(2n+1\right)}-\dfrac{1}{\left(2n+1\right).\left(2n+3\right)}\)
\(=\dfrac{1}{1.3}-\dfrac{1}{\left(2n+1\right).\left(2n+3\right)}\)
\(\Rightarrow E=\dfrac{\dfrac{1}{1.3}-\dfrac{1}{\left(2n+1\right).\left(2n+3\right)}}{4}\)
\(=\dfrac{1}{12}-\dfrac{1}{\left(2n+1\right).\left(2n+3\right).4}\)