Welcome...: Techniques for adding the numbers

Wednesday, 14 November 2012

Techniques for adding the numbers

1.Techniques for adding the numbers 1 to 100

Sum from 1 to n = $\displaystyle{\frac{n(n+1)}{2}}$

Sum from 1 to 100 = $\displaystyle{\frac{100(100+1)}{2} = (50)(101) = 5050}$

2.Let's prove the second statement.

1 + 2² + 3² + ... + n² =

3.The sum of cubes

$\begin{eqnarray} 1 + 2 + 3 + 4 + \ldots + n & = & \frac{n(n + 1)}{2} \\ 1^3 + 2^3 + 3^3 + 4^3 + \ldots + n^3 & = & \left[\frac{n(n + 1)}{2}\right]^2 \end{eqnarray}$

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