Q&A for How to Sum the Integers from 1 to N

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What is the sum of the first n positive integers?

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This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

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The formula for the sum of the first n positive integers is n(n+1)/2. This formula works for consecutive integers.

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What is the sum of squares formula?

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The sum of squares is also known as the sum of squared deviation scores. The formula for calculating the sum of squares for a single set of scores is SS = ΣX^2 - ((ΣX)^2 / N).

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How do you find the sum of n terms?

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This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

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To find the sum of a series of arithmetic terms (that is, terms that increase or decrease by a constant amount each term), use the formula S˯n = n(a˯1 + a˯n)/2, where n is the number of terms, a˯1 is the first term in the sequence, and a˯n is the last term in the sequence.

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Who made this formula?

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Leonhard Euler was able to derive it while he was in school. Google it. It's a fun story.

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The sum of 4 consecutive even numbers is 60. What is the sum of the squares of these numbers?

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First, figure out what the 4 consecutive even numbers are. Let's call the first one x. The next three will equal x + 2, x + 4, and x + 6. x+(x+2)+(x+4)+(x+6)=60 4x+12=60 4x=48 x=12 So the four numbers are 12, 14, 16, 18. Now just square each of these and add them up: 12*12+14*14+16*16+18*18 = 920.

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The sum of three consecutive odd numbers is 219. Can you help me find the three numbers?

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71, 73, 75. x+(x+2)+(x+4) = 219. 3x+6 = 219. 3x = 219-6. 3x = 213. x = 71. Then distribute.

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How do I find 7 consecutive integers whose sum is zero?

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Assuming that zero is considered an integer, it would be -3, -2, -1, 0, 1, 2, and 3.

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How can I find three integers such that ten times the sum of the integers is the same as six times the second integer?

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You don't have enough information to find the answer.

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How do I find integers that are divisible?

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Let's pretend the integer is N and the "divisible by" number is M. If N divided by M is a whole number, then N is divisible by M. If N divided by M is not a whole number, N is not divisible by M.

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How do I find how many times 2 will divide the product of all the whole numbers from 1 to 50?

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This is rather a case of factorials than sums; therefore, you'll be required to divide the factorial of 50 by 2. 50!/2 = (3.041409E64)/2 =1.520705E64.

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How do I add the numbers from 20 to 35?

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Use the relevant formula in the above article to add the integers from 1 to 35. Then separately add the integers from 1 to 19. Subtract the second sum from the first.

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What are two integers of root 45?

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The square root of 45 is 6.7082.

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How do I find the sum of integers between square 18 and square 53?

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You can't actually find the sum. While the square of 18 is 9 (an integer), the square of 53 is 7.2 which isn't an integer.

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The square of the sum of a number and two is 49. What are the numbers that satisfy the condition?

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(n + 2)² = 49. Take the square root of both sides of the equation: (n + 2) = +/- 7. When (n + 2) equals +7, n = 5. When (n + 2) = -7, n = -9. The condition is satisfied when n is either 5 or -9.

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