Find the sum of consecutive integers Calculus

What is the value of the following sums?

\sum_{i=4}^{11}i

60

64

52

73

\sum_{i=10}^{50}i

940

1380

1230

1170

\sum_{i=5}^{150}i

8,227

10,340

9,240

11,315

\sum_{i=-10}^{100}i

4230

4995

3570

5470

\sum_{i=1}^{k_1}i

\dfrac{k_1^2}{2}

5435

\dfrac{n\left(n+1\right)}{2}

\dfrac{k_1\left(k_1+1\right)}{2}

\sum_{i=5}^{k_1}i

\dfrac{k_1}{3}-50

\dfrac{k_1\left(k_1+1\right)}{4}-100

\dfrac{k_1\left(k_1+1\right)}{2}-10

\dfrac{k_1\left(k_1+1\right)}{3}-50

\sum_{i=k_1}^{100}i, 0 \lt k_1 \lt 100

4\ 550-\dfrac{k_1\left(k_1-1\right)}{2}

5\ 050-\dfrac{k_1\left(k_1+1\right)}{2}

3\ 540-\dfrac{k_1\left(k_1+1\right)}{3}

4\ 600-\dfrac{k_1\left(k_1+1\right)}{2}