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4 years ago

How to divide 900,000 divide 1000

Mathematics

1 answer:

Leni [432]4 years ago

7 0

Answer: 900

Step-by-step explanation:

To divide 900,000 by 1,000 it might be easier to write it as a fraction:

$\frac{900,000}{1,000}$

After doing this, you can cross out the same number of zeros on the numerator and denominator. Since there are three zeros in the denominator, cross out three on the top and bottom. MAKE SURE YOU DON'T CROSS OUT MORE THAN THREE ZEROS IN THE TOP! Always cross out the smallest number of zeros. Also keep in mind that this is only for zeros, not any other number.

$\frac{900}{1}$

Also, there are multiple ways to divide this number but this is one of the easiest ways (other than plugging it in a calculator).

Hope this helps!

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What is the sum of the first 51 consecutive odd positive integers?

Angelina_Jolie [31]

We call:

$a_{n}$ as the set of the first 51 consecutive odd positive integers, so:

 $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

 $a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}$

Then:

 $a_{n} = a_{1} + (n-1)d$

So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

 $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$

Therefore, we need to find:
 $a_{k} = a_{51}$

Given that $a_{1} = 1$ , then:

$a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1$

Thus:
$a_{k} = a_{51} = 2(51)-1 = 101$

Lastly:

$S_{51} = ( \frac{1 + 101}{2} ).51 = 2601$

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Answer:

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