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

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

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

expand

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

\frac{n}{2} + 2^{n - 2} n

Solution steps

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

Remove parentheses:

(a) = a

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

Multiply fractions:

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

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

\frac{2 ^{n - 1} n}{2} : 2^{n - 2} n

= \frac{n}{2} + 2^{n - 2} n

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