erweitern ((11e)/(30)+5/7)^5

Lösung

erweitern

(\frac{11 e}{30} + \frac{5}{7})^{5}

\frac{161051 e ^{5}}{24300000} + \frac{14641 e ^{4}}{226800} + \frac{1331 e ^{3}}{5292} + \frac{3025 e ^{2}}{6174} + \frac{6875 e}{14406} + \frac{3125}{16807}

Dezimale

14.66344 \dots

Schritte zur Lösung

(\frac{11 e}{30} + \frac{5}{7})^{5}

Wende Binomialsetz an:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = \frac{11 e}{30}, b = \frac{5}{7}

= i = 0 \sum 5 (i 5) (\frac{11 e}{30})^{(5 - i)} (\frac{5}{7})^{i}

Erweitere Summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (\frac{11 e}{30})^{5} (\frac{5}{7})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (\frac{11 e}{30})^{4} (\frac{5}{7})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (\frac{11 e}{30})^{3} (\frac{5}{7})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (\frac{11 e}{30})^{2} (\frac{5}{7})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (\frac{11 e}{30})^{1} (\frac{5}{7})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (\frac{11 e}{30})^{0} (\frac{5}{7})^{5}

\frac{5 !}{0 ! ( 5 - 0 ) !} (\frac{11 e}{30})^{5} (\frac{5}{7})^{0} = \frac{161051 e ^{5}}{24300000}

\frac{5 !}{1 ! ( 5 - 1 ) !} (\frac{11 e}{30})^{4} (\frac{5}{7})^{1} = \frac{14641 e ^{4}}{226800}

\frac{5 !}{2 ! ( 5 - 2 ) !} (\frac{11 e}{30})^{3} (\frac{5}{7})^{2} = \frac{1331 e ^{3}}{5292}

\frac{5 !}{3 ! ( 5 - 3 ) !} (\frac{11 e}{30})^{2} (\frac{5}{7})^{3} = \frac{3025 e ^{2}}{6174}

\frac{5 !}{4 ! ( 5 - 4 ) !} (\frac{11 e}{30})^{1} (\frac{5}{7})^{4} = \frac{6875 e}{14406}

\frac{5 !}{5 ! ( 5 - 5 ) !} (\frac{11 e}{30})^{0} (\frac{5}{7})^{5} = \frac{3125}{16807}

= \frac{161051 e ^{5}}{24300000} + \frac{14641 e ^{4}}{226800} + \frac{1331 e ^{3}}{5292} + \frac{3025 e ^{2}}{6174} + \frac{6875 e}{14406} + \frac{3125}{16807}

e x p an d (x^{2} + \frac{1}{x})^{5}

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

e x p an d \frac{( 12 - x ) ^{2}}{4}

e x p an d (t + 1) cos (2 t)

s im pl i f y - 5 (m + \frac{1}{3})