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If You Know What I Mean's question at Yahoo! Answers regarding summations

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MarkFL

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Feb 24, 2012
13,775
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MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Hello If You Know What I Mean,

For these two questions, we will rely on the formula:

\(\displaystyle \sum_{k=1}^nk=\frac{n(n+1)}{2}\)

We will factor out the integer $m$ which divides each term, leaving a summation of sequential natural numbers, whose upper limit of summation is determined by \(\displaystyle \left\lfloor\frac{101}{m} \right\rfloor\). Hence, we find:

a) \(\displaystyle S=2\sum_{k=1}^{50}k=2\cdot\frac{50(50+1)}{2}=50 \cdot51=2550\)

b) \(\displaystyle S=5\sum_{k=1}^{20}k=5\cdot\frac{20(20+1)}{2}=50 \cdot21=1050\)

To If You Know What I Mean and any other guests viewing this topic, I invite and encourage you to post other summation of arithmetic series questions in our Pre-Algebra and Algebra forum.

Best Regards,

Mark.