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受欢迎的代数 >

展开 (0.25+0.75e^t)^5

解答

展开

(0.25 + 0.75 e^{t})^{5}

解答

0.0009765625 + 0.01464 \dots e^{t} + 0.087890625 e^{2 t} + 0.263671875 e^{3 t} + 0.3955078125 e^{4 t} + 0.2373046875 e^{5 t}

求解步骤

(0.25 + 0.75 e^{t})^{5}

使用二项式定理:

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

a = 0.25, b = 0.75 e^{t}

= i = 0 \sum 5 (i 5) \cdot 0.2 5^{(5 - i)} (0.75 e^{t})^{i}

展开求和

= \frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 0.2 5^{5} (0.75 e^{t})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 0.2 5^{4} (0.75 e^{t})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 0.2 5^{3} (0.75 e^{t})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 0.2 5^{2} (0.75 e^{t})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 0.2 5^{1} (0.75 e^{t})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 0.2 5^{0} (0.75 e^{t})^{5}

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 0.2 5^{5} (0.75 e^{t})^{0} = 0.0009765625

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 0.2 5^{4} (0.75 e^{t})^{1} : 0.0146484375 e^{t}

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 0.2 5^{3} (0.75 e^{t})^{2} : 0.087890625 e^{2 t}

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 0.2 5^{2} (0.75 e^{t})^{3} : 0.263671875 e^{3 t}

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 0.2 5^{1} (0.75 e^{t})^{4} : 0.3955078125 e^{4 t}

化简

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 0.2 5^{0} (0.75 e^{t})^{5} : 0.2373046875 e^{5 t}

= 0.0009765625 + 0.01464 \dots e^{t} + 0.087890625 e^{2 t} + 0.263671875 e^{3 t} + 0.3955078125 e^{4 t} + 0.2373046875 e^{5 t}

流行的例子

展开 ((x+1)y)/x

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

展开 (-2,-6)y(12,18)

e x p an d (- 2, - 6) y (12, 18)

展开 (sqrt(x)-1)^2dx

e x p an d (x - 1)^{2} d x

展开 (6,6)y(6,-6)

e x p an d (6, 6) y (6, - 6)

化简 \delta(n-5)

s im pl i f y δ (n - 5)