erweitern ((n+1)^2)/(n^3)

Lösung

erweitern

\frac{( n + 1 ) ^{2}}{n ^{3}}

\frac{1}{n} + \frac{2}{n ^{2}} + \frac{1}{n ^{3}}

Schritte zur Lösung

\frac{( n + 1 ) ^{2}}{n ^{3}}

(n + 1)^{2} = n^{2} + 2 n + 1

= \frac{n ^{2} + 2 n + 1}{n ^{3}}

Wende Bruchregel an:

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

\frac{n ^{2} + 2 n + 1}{n ^{3}} = \frac{n ^{2}}{n ^{3}} + \frac{2 n}{n ^{3}} + \frac{1}{n ^{3}}

= \frac{n ^{2}}{n ^{3}} + \frac{2 n}{n ^{3}} + \frac{1}{n ^{3}}

Streiche

\frac{n ^{2}}{n ^{3}} : \frac{1}{n}

= \frac{1}{n} + \frac{2 n}{n ^{3}} + \frac{1}{n ^{3}}

Streiche

\frac{2 n}{n ^{3}} : \frac{2}{n ^{2}}

= \frac{1}{n} + \frac{2}{n ^{2}} + \frac{1}{n ^{3}}

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