erweitern (n+1/n)^3

Lösung

erweitern

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

\frac{n ^{6} + 3 n ^{4} + 3 n ^{2} + 1}{n ^{3}}

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Vereinfache

n^{3} + 3 n^{2} \frac{1}{n} + 3 n (\frac{1}{n})^{2} + (\frac{1}{n})^{3} : \frac{n ^{6} + 3 n ^{4} + 3 n ^{2} + 1}{n ^{3}}

= \frac{n ^{6} + 3 n ^{4} + 3 n ^{2} + 1}{n ^{3}}

s im pl i f y (cos (x) + i sin (x))^{7}

e x p an d \frac{x}{( 1 + x ^{2} ) ^{2}}

e x p an d \frac{sin ( z )}{( z - 1 ) ( z + 1 ) ^{2}}

e x p an d x (x + 2)^{2}

e x p an d (3 x^{4} - y) d x + (x - 4 x^{2} y^{3}) d y