What is expand (n(n+1))/2+(n+1) ?

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

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expand (n(n+1))/2+(n+1)

expand

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

Expand

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

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

Apply the fraction rule:

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

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

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

\frac{6}{( s - 2 ) ^{4}}

\frac{1}{s ( T s + 1 )}

\frac{( 3 x + 1 ) ( x ^{2} + 4 x - 32 )}{( 3 x ^{2} + 25 x - 8 ) ( x + 4 )}

(- 1 + 3 i)^{4}

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

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