What is (((-1)^{n-1})((3/2)^n))/((n^2)) ?

The solution to (((-1)^{n-1})((3/2)^n))/((n^2)) is (3^n(-1)^{n-1})/(2^nn^2)

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simplify (((-1)^{n-1})((3/2)^n))/((n^2))

simplify

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

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

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

Multiply

(- 1)^{n - 1} \frac{3 ^{n}}{2 ^{n}} : \frac{3 ^{n} ( - 1 ) ^{n - 1}}{2 ^{n}}

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

Apply the fraction rule:

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

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

\frac{( 5 x ^{2} \cdot y )}{( 5 x )}

5 t^{2} + 3 t^{2} + 8 t

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

3 x^{3} + 8 x^{2} + 3 x - 2

4.5 (3^{2}) - 4.5 n + 3

What is (((-1)^{n-1})((3/2)^n))/((n^2)) ?
The solution to (((-1)^{n-1})((3/2)^n))/((n^2)) is (3^n(-1)^{n-1})/(2^nn^2)