erweitern (5^{n-1})/((n+1)^24^n)

Lösung

erweitern

\frac{5 ^{n - 1}}{( n + 1 ) ^{2} 4 ^{n}}

\frac{5 ^{n - 1}}{4 ^{n} n ^{2} + 2 ^{1 + 2 n} n + 4 ^{n}}

Schritte zur Lösung

\frac{5 ^{n - 1}}{( n + 1 ) ^{2} \cdot 4 ^{n}}

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

= \frac{5 ^{n - 1}}{4 ^{n} ( n ^{2} + 2 n + 1 )}

Multipliziere aus

(n^{2} + 2 n + 1) \cdot 4^{n} : 4^{n} n^{2} + 2^{1 + 2 n} n + 4^{n}

= \frac{5 ^{n - 1}}{4 ^{n} n ^{2} + 2 ^{2 n + 1} n + 4 ^{n}}

e x p an d 5 (x^{2} + y^{2}) e^{y^{2} - x^{2}}

e x p an d \frac{a ^{2} + 4 a + 4}{( 3 a + 3 b ) ( a + b )}

e x p an d \frac{3 x ^{2} + 1}{( x + 2 ) ^{3}}

e x p an d - \frac{6 ( u ^{2} - 2 )}{( u ^{2} + 2 ) ^{2}}

e x p an d 4 (\frac{1}{2} (x - y))^{2} + 2 (x + y)^{2}