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

Staff member

#### MarkFL

Staff member
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.