erweitern ((1000+n^2)^2)/(1000000)

Lösung

erweitern

\frac{( 1000 + n ^{2} ) ^{2}}{1000000}

1 + \frac{n ^{2}}{500} + \frac{n ^{4}}{1000000}

Schritte zur Lösung

\frac{( 1000 + n ^{2} ) ^{2}}{1000000}

(1000 + n^{2})^{2} = 1000000 + 2000 n^{2} + n^{4}

= \frac{1000000 + 2000 n ^{2} + n ^{4}}{1000000}

Wende Bruchregel an:

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

\frac{1000000 + 2000 n ^{2} + n ^{4}}{1000000} = \frac{1000000}{1000000} + \frac{2000 n ^{2}}{1000000} + \frac{n ^{4}}{1000000}

= \frac{1000000}{1000000} + \frac{2000 n ^{2}}{1000000} + \frac{n ^{4}}{1000000}

Wende Regel an

\frac{a}{a} = 1

\frac{1000000}{1000000} = 1

= 1 + \frac{2000 n ^{2}}{1000000} + \frac{n ^{4}}{1000000}

Streiche

\frac{2000 n ^{2}}{1000000} : \frac{n ^{2}}{500}

= 1 + \frac{n ^{2}}{500} + \frac{n ^{4}}{1000000}

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