erweitern (9(n+1)(2n+1))/(2n^2)

Lösung

erweitern

\frac{9 ( n + 1 ) ( 2 n + 1 )}{2 n ^{2}}

9 + \frac{27}{2 n} + \frac{9}{2 n ^{2}}

Schritte zur Lösung

\frac{9 ( n + 1 ) ( 2 n + 1 )}{2 n ^{2}}

Multipliziere aus

9 (n + 1) (2 n + 1) : 18 n^{2} + 27 n + 9

= \frac{18 n ^{2} + 27 n + 9}{2 n ^{2}}

Wende Bruchregel an:

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

\frac{18 n ^{2} + 27 n + 9}{2 n ^{2}} = \frac{18 n ^{2}}{2 n ^{2}} + \frac{27 n}{2 n ^{2}} + \frac{9}{2 n ^{2}}

= \frac{18 n ^{2}}{2 n ^{2}} + \frac{27 n}{2 n ^{2}} + \frac{9}{2 n ^{2}}

Streiche

\frac{18 n ^{2}}{2 n ^{2}} : 9

= 9 + \frac{27 n}{2 n ^{2}} + \frac{9}{2 n ^{2}}

Streiche

\frac{27 n}{2 n ^{2}} : \frac{27}{2 n}

= 9 + \frac{27}{2 n} + \frac{9}{2 n ^{2}}

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