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

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

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expand (k(k+1))/2+(k+1)

expand

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

Expand

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

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

Apply the fraction rule:

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

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

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

2 x^{2} - 11 = 0

\frac{2 x + 4}{3} = \frac{x}{6} - 3

x^{16} - y^{18}

\frac{3 x ^{3}}{6 y ^{3}} \cdot \frac{y ^{5}}{x ^{5}}

16 \geq 6 + \frac{x}{2}

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