What is expand (1+sqrt(5))^{14} ?

The solution to expand (1+sqrt(5))^{14} is 6905856+3088384sqrt(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (1+sqrt(5))^{14}

expand

(1 + 5)^{14}

6905856 + 30883845

Decimal Notation

13811692.56462 \dots

Solution steps

(1 + 5)^{14}

Apply binomial theorem:

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

a = 1, b = 5

= i = 0 \sum 14 (i 14) \cdot 1^{(14 - i)} (5)^{i}

Expand summation

= \frac{14 !}{0 ! ( 14 - 0 ) !} \cdot 1^{14} (5)^{0} + \frac{14 !}{1 ! ( 14 - 1 ) !} \cdot 1^{13} (5)^{1} + \frac{14 !}{2 ! ( 14 - 2 ) !} \cdot 1^{12} (5)^{2} + \frac{14 !}{3 ! ( 14 - 3 ) !} \cdot 1^{11} (5)^{3} + \frac{14 !}{4 ! ( 14 - 4 ) !} \cdot 1^{10} (5)^{4} + \frac{14 !}{5 ! ( 14 - 5 ) !} \cdot 1^{9} (5)^{5} + \frac{14 !}{6 ! ( 14 - 6 ) !} \cdot 1^{8} (5)^{6} + \frac{14 !}{7 ! ( 14 - 7 ) !} \cdot 1^{7} (5)^{7} + \frac{14 !}{8 ! ( 14 - 8 ) !} \cdot 1^{6} (5)^{8} + \frac{14 !}{9 ! ( 14 - 9 ) !} \cdot 1^{5} (5)^{9} + \frac{14 !}{10 ! ( 14 - 10 ) !} \cdot 1^{4} (5)^{10} + \frac{14 !}{11 ! ( 14 - 11 ) !} \cdot 1^{3} (5)^{11} + \frac{14 !}{12 ! ( 14 - 12 ) !} \cdot 1^{2} (5)^{12} + \frac{14 !}{13 ! ( 14 - 13 ) !} \cdot 1^{1} (5)^{13} + \frac{14 !}{14 ! ( 14 - 14 ) !} \cdot 1^{0} (5)^{14}

Simplify

\frac{14 !}{0 ! ( 14 - 0 ) !} \cdot 1^{14} (5)^{0} : 1

Simplify

\frac{14 !}{1 ! ( 14 - 1 ) !} \cdot 1^{13} (5)^{1} : 145

Simplify

\frac{14 !}{2 ! ( 14 - 2 ) !} \cdot 1^{12} (5)^{2} : 455

Simplify

\frac{14 !}{3 ! ( 14 - 3 ) !} \cdot 1^{11} (5)^{3} : 18205

Simplify

\frac{14 !}{4 ! ( 14 - 4 ) !} \cdot 1^{10} (5)^{4} : 25025

Simplify

\frac{14 !}{5 ! ( 14 - 5 ) !} \cdot 1^{9} (5)^{5} : 500505

Simplify

\frac{14 !}{6 ! ( 14 - 6 ) !} \cdot 1^{8} (5)^{6} : 375375

Simplify

\frac{14 !}{7 ! ( 14 - 7 ) !} \cdot 1^{7} (5)^{7} : 4290005

Simplify

\frac{14 !}{8 ! ( 14 - 8 ) !} \cdot 1^{6} (5)^{8} : 1876875

Simplify

\frac{14 !}{9 ! ( 14 - 9 ) !} \cdot 1^{5} (5)^{9} : 12512505

Simplify

\frac{14 !}{10 ! ( 14 - 10 ) !} \cdot 1^{4} (5)^{10} : 3128125

Simplify

\frac{14 !}{11 ! ( 14 - 11 ) !} \cdot 1^{3} (5)^{11} : 11375005

Simplify

\frac{14 !}{12 ! ( 14 - 12 ) !} \cdot 1^{2} (5)^{12} : 1421875

Simplify

\frac{14 !}{13 ! ( 14 - 13 ) !} \cdot 1^{1} (5)^{13} : 2187505

Simplify

\frac{14 !}{14 ! ( 14 - 14 ) !} \cdot 1^{0} (5)^{14} : 78125

= 1 + 145 + 455 + 18205 + 25025 + 500505 + 375375 + 4290005 + 1876875 + 12512505 + 3128125 + 11375005 + 1421875 + 2187505 + 78125

1 + 145 + 455 + 18205 + 25025 + 500505 + 375375 + 4290005 + 1876875 + 12512505 + 3128125 + 11375005 + 1421875 + 2187505 + 78125 = 6905856 + 30883845

= 6905856 + 30883845

- \frac{5 ( e ^{- 6 s} - 1 )}{s}

(2 x + 4 y^{2}) (2 x - 4 y^{2})

(x - 7) (x + \frac{14}{3})

\frac{2 x ( x ^{3} + 2 )}{x ^{2} + 3} + 3 x^{2} ln (x^{2} + 3)

ln (x^{3} + 2)

What is expand (1+sqrt(5))^{14} ?
The solution to expand (1+sqrt(5))^{14} is 6905856+3088384sqrt(5)