What is (1+1/(n+1))(1-n/((n+1)^2)) ?

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

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simplify (1+1/(n+1))(1-n/((n+1)^2))

simplify

(1 + \frac{1}{n + 1}) (1 - \frac{n}{( n + 1 ) ^{2}})

\frac{( n + 2 ) ( n ^{2} + n + 1 )}{( n + 1 ) ^{3}}

Solution steps

(1 + \frac{1}{n + 1}) (1 - \frac{n}{( n + 1 ) ^{2}})

Join

1 + \frac{1}{n + 1} : \frac{n + 2}{n + 1}

= \frac{n + 2}{n + 1} (1 - \frac{n}{( n + 1 ) ^{2}})

Apply the fraction rule:

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

= \frac{( n + 2 ) ( 1 - \frac{n}{( n + 1 ) ^{2}} )}{n + 1}

Simplify

(n + 2) (1 - \frac{n}{( n + 1 ) ^{2}}) : \frac{( n + 2 ) ( n ^{2} + n + 1 )}{( n + 1 ) ^{2}}

= \frac{\frac{( n + 2 ) ( n ^{2} + n + 1 )}{( n + 1 ) ^{2}}}{n + 1}

Apply the fraction rule:

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

= \frac{( n + 2 ) ( n ^{2} + n + 1 )}{( n + 1 ) ^{2} ( n + 1 )}

Simplify

(n + 1)^{2} (n + 1) : (n + 1)^{3}

= \frac{( n + 2 ) ( n ^{2} + n + 1 )}{( n + 1 ) ^{3}}

ln (x) (x + 2)

(1 - x) d x

lo g_{10} (x^{5} y^{- 10})

\frac{( 1 + 2 e ^{t} ) ^{3}}{27}

\frac{I n ( 2 - 3 x )}{x ^{2} - 36}

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