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

[MarkFL]

Here is the question:

How with sequence question?

find the sum of all integers between 0 an 101 that are divisible by a)2 b)5

thanks

Here is a link to the question:

How with sequence question? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

 

[MarkFL]

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 http://www.mathhelpboards.com/f2/ forum.

Best Regards,

Mark.