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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

Schreibe

(n + 1)^{2}

um:

n^{2} + 2 n + 1

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

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

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

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

Apply rule:

a \cdot 1 = a

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

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

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