erweitern 1-(1/((1+x)^{20)})

Lösung

erweitern

1 - (\frac{1}{( 1 + x ) ^{20}})

1 - \frac{1}{1 + 20 x + 190 x ^{2} + 1140 x ^{3} + 4845 x ^{4} + 15504 x ^{5} + 38760 x ^{6} + 77520 x ^{7} + 125970 x ^{8} + 167960 x ^{9} + 184756 x ^{10} + 167960 x ^{11} + 125970 x ^{12} + 77520 x ^{13} + 38760 x ^{14} + 15504 x ^{15} + 4845 x ^{16} + 1140 x ^{17} + 190 x ^{18} + 20 x ^{19} + x ^{20}}

Schritte zur Lösung

1 - (\frac{1}{( 1 + x ) ^{20}})

Entferne die Klammern:

(a) = a

= 1 - \frac{1}{( 1 + x ) ^{20}}

(1 + x)^{20} = 1 + 20 x + 190 x^{2} + 1140 x^{3} + 4845 x^{4} + 15504 x^{5} + 38760 x^{6} + 77520 x^{7} + 125970 x^{8} + 167960 x^{9} + 184756 x^{10} + 167960 x^{11} + 125970 x^{12} + 77520 x^{13} + 38760 x^{14} + 15504 x^{15} + 4845 x^{16} + 1140 x^{17} + 190 x^{18} + 20 x^{19} + x^{20}

= 1 - \frac{1}{x ^{20} + 20 x ^{19} + 190 x ^{18} + 1140 x ^{17} + 4845 x ^{16} + 15504 x ^{15} + 38760 x ^{14} + 77520 x ^{13} + 125970 x ^{12} + 167960 x ^{11} + 184756 x ^{10} + 167960 x ^{9} + 125970 x ^{8} + 77520 x ^{7} + 38760 x ^{6} + 15504 x ^{5} + 4845 x ^{4} + 1140 x ^{3} + 190 x ^{2} + 20 x + 1}

e x p an d \frac{3 - 5 a - 5 h + 4 ( a + h ) ^{2}}{h}

e x p an d 5 + 4 (2 x - 1 = 17)

e x p an d - sin (2 π f (x - a))

e x p an d ∣ f (x - 5) - 10 ∣

e x p an d (8 x^{2} - 6 x - 3) - (9 x^{2} + 7 x = 5)