What is expand ((n+1)^4)/(3n^4) ?

The solution to expand ((n+1)^4)/(3n^4) is 1/3+4/(3n)+2/(n^2)+4/(3n^3)+1/(3n^4)

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expand ((n+1)^4)/(3n^4)

expand

\frac{( n + 1 ) ^{4}}{3 n ^{4}}

\frac{1}{3} + \frac{4}{3 n} + \frac{2}{n ^{2}} + \frac{4}{3 n ^{3}} + \frac{1}{3 n ^{4}}

Solution steps

\frac{( n + 1 ) ^{4}}{3 n ^{4}}

(n + 1)^{4} = n^{4} + 4 n^{3} + 6 n^{2} + 4 n + 1

= \frac{n ^{4} + 4 n ^{3} + 6 n ^{2} + 4 n + 1}{3 n ^{4}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{n ^{4} + 4 n ^{3} + 6 n ^{2} + 4 n + 1}{3 n ^{4}} = \frac{n ^{4}}{3 n ^{4}} + \frac{4 n ^{3}}{3 n ^{4}} + \frac{6 n ^{2}}{3 n ^{4}} + \frac{4 n}{3 n ^{4}} + \frac{1}{3 n ^{4}}

= \frac{n ^{4}}{3 n ^{4}} + \frac{4 n ^{3}}{3 n ^{4}} + \frac{6 n ^{2}}{3 n ^{4}} + \frac{4 n}{3 n ^{4}} + \frac{1}{3 n ^{4}}

\frac{n ^{4}}{3 n ^{4}} = \frac{1}{3}

\frac{4 n ^{3}}{3 n ^{4}} = \frac{4}{3 n}

\frac{6 n ^{2}}{3 n ^{4}} = \frac{2}{n ^{2}}

\frac{4 n}{3 n ^{4}} = \frac{4}{3 n ^{3}}

= \frac{1}{3} + \frac{4}{3 n} + \frac{2}{n ^{2}} + \frac{4}{3 n ^{3}} + \frac{1}{3 n ^{4}}

\frac{d ^{2}}{d x ^{2}} ((y) (\frac{4 x ^{5}}{5} - 7 x))

4 \cdot (t - 1) \cdot e^{- 0.5 \cdot t} + 8

\frac{ln ( 2 ) ( - \frac{1}{2} ) - 1}{2}

\frac{6 x ( y - 1 ) ^{3}}{2 x ^{2} + ( y - 1 ) ^{6}}

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What is expand ((n+1)^4)/(3n^4) ?
The solution to expand ((n+1)^4)/(3n^4) is 1/3+4/(3n)+2/(n^2)+4/(3n^3)+1/(3n^4)