What is (n(n+1)}{2*(n\frac{(n+1))/2)^2} ?

The solution to (n(n+1)}{2*(n\frac{(n+1))/2)^2} is 2/(n(n+1))

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simplify (n(n+1)}{2*(n\frac{(n+1))/2)^2}

simplify

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

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

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

n^{2} = nn

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

Cancel the common factor:

n

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

Simplify

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

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

\frac{x ^{\frac{1}{2}} \cdot x ^{- 3}}{2}

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y^{- 3} x^{6} + y^{6} x^{- 3}

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(\frac{3 m ^{4} n ^{5}}{6 n ^{2}})^{3}

What is (n(n+1)}{2*(n\frac{(n+1))/2)^2} ?
The solution to (n(n+1)}{2*(n\frac{(n+1))/2)^2} is 2/(n(n+1))