# Summation problem (first N positive integers)

• GeorgeCostanz
In summary, the formula for the sum of the first N positive integers is n^2(n+1)/2, where n is the value of the upper bound in the summation. To reduce this formula, you can start with the innermost summation and work your way out. Keep in mind that the upper bound for the second summation should be "i" and not "n".
GeorgeCostanz

## Homework Equations

so i kno the formula for the for the sum of the first N positive integers

when i = 1

## The Attempt at a Solution

i kno the answer = n^2(n+1)/2

but could someone explain step by step how you reduce it to get the final answer? as if I'm in kindergarten? I'm slow, thanks.

my work:

following the formula: n(n+1)/2 * n(n+1)/2 * n(n+1)/2 ?

i don't understand how to reduce the terms to get the final answer provided

Last edited:
GeorgeCostanz said:

## Homework Equations

so i kno the formula for the for the sum of the first N positive integers

when i = 1

## The Attempt at a Solution

i kno the answer = n^2(n+1)/2

but could someone explain step by step how you reduce it to get the final answer? as if I'm in kindergarten? I'm slow, thanks.

PF rules require you to show us your work.

oh okay sure

Are you sure the upper bound on the second summation is "i" and not "n"? Note that this is a summation of the value "1", not the variable "i".

rcgldr said:
Are you sure the upper bound on the second summation is "i" and not "n"? Note that this is a summation of the value "1", not the variable "i".

If the upper bound on the second summation were "n" then the sum would be n^3. You are only going to get the correct answer if the upper bound is "i". Start with the innermost sum and work your way out. It's not hard.

## What is a summation problem (first N positive integers)?

A summation problem (first N positive integers) is a mathematical problem that involves finding the sum of the first N positive integers. This can be represented as 1 + 2 + 3 + ... + N. It is often used to calculate the total number of items or values in a given set.

## How do you solve a summation problem (first N positive integers)?

To solve a summation problem (first N positive integers), you can use the formula: (N x (N + 1)) / 2. This formula is also known as the Gauss formula. Simply plug in the value of N and solve the equation to find the sum.

## What is the significance of the Gauss formula in solving summation problems?

The Gauss formula is significant because it provides a quick and efficient way to solve summation problems. It is based on a pattern observed by mathematician Carl Friedrich Gauss, and can be used to find the sum of any consecutive sequence of numbers, not just the first N positive integers.

## Can summation problems (first N positive integers) be solved using any other method?

Yes, there are other methods that can be used to solve summation problems (first N positive integers). For example, you can also use a mathematical technique called "telescoping" to find the sum. This involves manipulating the terms in the sum to simplify the equation and make it easier to solve.

## What are some real-life applications of summation problems (first N positive integers)?

Summation problems (first N positive integers) have various real-life applications, including in finance, physics, and computer science. For example, in finance, it can be used to calculate the total return on an investment over a period of time. In physics, it can be used to calculate the total displacement of an object over a certain time period. In computer science, it can be used to analyze and optimize algorithms that involve adding a large number of values.

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