What is expand ((2n+1)x^{2n})/((2n+1)!) ?

The solution to expand ((2n+1)x^{2n})/((2n+1)!) is (2nx^{2n})/((2n+1)!)+(x^{2n})/((2n+1)!)

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expand ((2n+1)x^{2n})/((2n+1)!)

expand

\frac{( 2 n + 1 ) x ^{2 n}}{( 2 n + 1 ) !}

\frac{2 n x ^{2 n}}{( 2 n + 1 ) !} + \frac{x ^{2 n}}{( 2 n + 1 ) !}

Solution steps

\frac{( 2 n + 1 ) x ^{2 n}}{( 2 n + 1 ) !}

Expand

(2 n + 1) x^{2 n} : 2 n x^{2 n} + x^{2 n}

= \frac{2 n x ^{2 n} + x ^{2 n}}{( 2 n + 1 ) !}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 n x ^{2 n} + x ^{2 n}}{( 2 n + 1 ) !} = \frac{2 n x ^{2 n}}{( 2 n + 1 ) !} + \frac{x ^{2 n}}{( 2 n + 1 ) !}

= \frac{2 n x ^{2 n}}{( 2 n + 1 ) !} + \frac{x ^{2 n}}{( 2 n + 1 ) !}

\frac{e ^{x}}{( e ^{x} - e ^{2} ) ^{2}}

\frac{1}{( 1 - i w ) ^{2}}

e^{π 2 (1 + i)}

\frac{248 ( 16 + 56 4 - 1 )}{15}

so l v e (x^{2} + 4 x - 5)

What is expand ((2n+1)x^{2n})/((2n+1)!) ?
The solution to expand ((2n+1)x^{2n})/((2n+1)!) is (2nx^{2n})/((2n+1)!)+(x^{2n})/((2n+1)!)