What is expand ((-1)^{k+1}k(k+1))/2 ?

The solution to expand ((-1)^{k+1}k(k+1))/2 is ((-1)^{k+1}k^2)/2+((-1)^{k+1}k)/2

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expand ((-1)^{k+1}k(k+1))/2

expand

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

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

Solution steps

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

Expand

(- 1)^{k + 1} k (k + 1) : (- 1)^{k + 1} k^{2} + (- 1)^{k + 1} k

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

Apply the fraction rule:

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

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

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

e^{x} (e^{y} + e^{- x})

ln (x) (x + 1) (x + 2)

\frac{3}{( 2 + j w ) ( 5 + j w )}

(e - π)^{2}

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

What is expand ((-1)^{k+1}k(k+1))/2 ?
The solution to expand ((-1)^{k+1}k(k+1))/2 is ((-1)^{k+1}k^2)/2+((-1)^{k+1}k)/2