0
How do you find the sum of all the even positive integers up until n?
Mezappy8
An even integer is one that can be expressed in the from 2k where k is a number in the set of integers, so the summation of all even positive numbers up to n, assuming of course that n is even also, would look like this:
Σn/2k=1 (2k),which can be rewritten as 2Σn/2k=1 (k).
We have set n/2 as the value to which the sum goes up to as the number you want to go up to is n, not 2n, 2*(n/2) is of course, n. Doing this also ensures that n is even as only an even integer can be divided without remainder by 2.
Now, this is an arithmetic progression from 1 up to n/2 and all multiplied by 2. The standard equation for an arithmetic progression going from 1 to n is Sn=(a1+an)*n/2 so we take this formula and replace n with n/2, replace a1 with 2 and an with n, and multiply both sides by 2 to get 2Sn = 2(2+n)*n/4 = (2+n)*n/2 and now divide by 2 to get Sn=(2+n)*n/4 and there's your formula for finding the sum of all even numbers up to n.
example
2+4+6+8+10+12+14+16+18+20=110
S20 = (2+20)*20/4 = 22*5 = 110
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
The sum of the squares of two consecutive positive even integers is 340 Find the integers?
12 and 14.
Find the total of the first three even numbers?
The sum of the first three even positive integers is 2 + 4 + 6 = 12.
How do you do integers greatest to least?
Positive integers are greater than negative integers. For positive integers: * The integer with more digits is larger. * If two integers have the same length, compare the first digit. If the first digit is the same, compare the second digit, then the third, etc., until you find a difference. In each case, the integer with the larger digit (at the first position where you find a difference) is the larger one.
How do you find the sum of all the positive integers of a number?
By adding whatever you mean with "integers of a number".
Where can you find the number 15?
In a list of positive integers less than 20.
What is The sum of the squares of two consecutive positive even integers is 340 Find the integers?
The sum of the squares of two consecutive positive even integers is 340. Find the integers.
The sum of the squares of two consecutive positive even integers is 340 Find the integers?
12 and 14.
The sum of the square of two consecutive positive even integer is 340 Find the integers?
The integers are 12 and 14 (144+196=340)
What is the sum of all even integers from 2 to 500 inclusive?
The formula n*(n+1) is used to find the sum of n positive integers. Th sum of positive integers up to 500 can be calculated as 250*251=62,750.
Find the two consecutive positive integers is 132 find the integers?
The numbers are 65 and 67.
Find the total of the first three even numbers?
The sum of the first three even positive integers is 2 + 4 + 6 = 12.
How do you do integers greatest to least?
Positive integers are greater than negative integers. For positive integers: * The integer with more digits is larger. * If two integers have the same length, compare the first digit. If the first digit is the same, compare the second digit, then the third, etc., until you find a difference. In each case, the integer with the larger digit (at the first position where you find a difference) is the larger one.
The product of 2 positive consecutive even integers is 48 What is the smaller number?
The product of 2 consecutive positive number is 48. Find the 2 numbers
How do you find the sum of all the positive integers of a number?
By adding whatever you mean with "integers of a number".
Find three consecutive even integers whose sum is 72?
The even integers are 22, 24 and 26.
Where can you find the number 15?
In a list of positive integers less than 20.
The sum of four consecutive even integers is the same as the least of the integers Find the integers?
-4, -2, 0, and 2 are the four consecutive even integers. When you add them up they equal -4.
