Telescoping Sums and Products (Example 2)

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Telescoping Sums and Products (Example 2)

January 2, 2010 by Metroplex Math Circle

This time I will provide both the problem and solution in the continuing series from Dr. Andreescu’s lecture on Telescoping Sums and Products.

Example 2. Evaluate

$\displaystyle\sum^{n}_{k=2}k!(k^2+k+1)$

Example 2. Solution

We can write

$\displaystyle\sum^{n}_{k=1}k!(k^2+k+1)=\displaystyle\sum^{n}_{k=1}[(k+1)^2-k)]k!$

$=\displaystyle\sum^{n}_{k=1}[(k+1)!(k+1)-k!k]$

$=(n+1)!(n+1)-1$

Posted in problems | Tagged math circle, sums and products, Titu Andreescu | Leave a Comment

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Metroplex Math Circle

Mathematical Problem Solving in North Texas

Telescoping Sums and Products (Example 2)

Example 2. Evaluate

Example 2. Solution

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Metroplex Math Circle

Mathematical Problem Solving in North Texas

Telescoping Sums and Products (Example 2)

Example 2. Evaluate

Example 2. Solution

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