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受欢迎的代数 >

展开 (0.25+q)^7

解答

展开

(0.25 + q)^{7}

解答

\frac{1}{16384} + \frac{7 q}{4096} + \frac{0.041015625 q ^{2}}{2} + \frac{0.8203125 q ^{3}}{6} + \frac{3.28125 q ^{4}}{6} + \frac{2.625 q ^{5}}{2} + \frac{7 q ^{6}}{4} + q^{7}

求解步骤

(0.25 + q)^{7}

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 = q

= i = 0 \sum 7 (i 7) \cdot 0.2 5^{(7 - i)} q^{i}

展开求和

= \frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 0.2 5^{7} q^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 0.2 5^{6} q^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 0.2 5^{5} q^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 0.2 5^{4} q^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 0.2 5^{3} q^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 0.2 5^{2} q^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 0.2 5^{1} q^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 0.2 5^{0} q^{7}

化简

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 0.2 5^{7} q^{0} : 0.00006 \dots

化简

\frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 0.2 5^{6} q^{1} : 0.00170 \dots q

化简

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 0.2 5^{5} q^{2} : \frac{0.041015625 q ^{2}}{2}

化简

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 0.2 5^{4} q^{3} : \frac{0.8203125 q ^{3}}{6}

化简

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 0.2 5^{3} q^{4} : \frac{3.28125 q ^{4}}{6}

化简

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 0.2 5^{2} q^{5} : \frac{2.625 q ^{5}}{2}

化简

\frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 0.2 5^{1} q^{6} : 1.75 q^{6}

化简

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 0.2 5^{0} q^{7} : q^{7}

= 0.00006 \dots + 0.00170 \dots q + \frac{0.041015625 q ^{2}}{2} + \frac{0.8203125 q ^{3}}{6} + \frac{3.28125 q ^{4}}{6} + \frac{2.625 q ^{5}}{2} + 1.75 q^{6} + q^{7}

化简

0.00006 \dots + 0.00170 \dots q + \frac{0.041015625 q ^{2}}{2} + \frac{0.8203125 q ^{3}}{6} + \frac{3.28125 q ^{4}}{6} + \frac{2.625 q ^{5}}{2} + 1.75 q^{6} + q^{7} : \frac{1}{16384} + \frac{7 q}{4096} + \frac{0.041015625 q ^{2}}{2} + \frac{0.8203125 q ^{3}}{6} + \frac{3.28125 q ^{4}}{6} + \frac{2.625 q ^{5}}{2} + \frac{7 q ^{6}}{4} + q^{7}

= \frac{1}{16384} + \frac{7 q}{4096} + \frac{0.041015625 q ^{2}}{2} + \frac{0.8203125 q ^{3}}{6} + \frac{3.28125 q ^{4}}{6} + \frac{2.625 q ^{5}}{2} + \frac{7 q ^{6}}{4} + q^{7}

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