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

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The discussion addresses how to find the sum of all integers between 0 and 101 that are divisible by 2 and 5. For integers divisible by 2, the sum is calculated as 2550, while for those divisible by 5, the sum is 1050. The calculations utilize the formula for the sum of a sequence of natural numbers, factoring out the divisor. The thread encourages further questions on summation of arithmetic series. This provides a clear method for solving similar mathematical problems.
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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.
 
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Hello If You Know What I Mean,

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

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

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 $$\left\lfloor\frac{101}{m} \right\rfloor$$. Hence, we find:

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

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

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.
 
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