Numerical Verification of the Three Summation Formulae

"Verifying" one of §6's three summation formulas for a given positive integer $n$ means: compute the left-hand side by direct addition, compute the right-hand side by substituting the same $n$ into the formula, and confirm the two numbers are equal. This is different from — and much simpler than — proving the formula holds for every possible $n$ (which needs mathematical induction, outside this syllabus).

Worked demonstration, for $n=3$:

• $\sum_{i=1}^{3} i = 1+2+3 = 6$, and the formula gives $\dfrac{3(3+1)}{2}=\dfrac{12}{2}=6$ — equal. ✓
• $\sum_{i=1}^{3} i^2 = 1+4+9=14$, and the formula gives $\dfrac{3(4)(7)}{6}=\dfrac{84}{6}=14$ — equal. ✓
• $\sum_{i=1}^{3} i^3 = 1+8+27=36$, and the formula gives $\left(\dfrac{3(4)}{2}\right)^2=(6)^2=36$ — equal. ✓