Addition Series: Sum of Successive Terms

Thread starter rajeshmarndi
Start date Mar 29, 2015
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Addition

AI Thread Summary

The discussion focuses on deriving a formula for the sum of successive terms in a series that starts from (8+7+...+1) and continues down to 1. The user references the known formula for the sum of the first n natural numbers, n(n+1)/2, to build a more complex series. They aim to express the total sum as a combination of sums of squares and linear terms. The approach involves calculating the sum of k(k+1) for k from 1 to n, leading to a formula that incorporates both the sum of squares and the sum of integers. The conversation emphasizes the mathematical manipulation of series to achieve the desired result.

Mar 29, 2015

rajeshmarndi

Homework Statement

I want to have a formula of this kind,
(8+7+...+1) + (7+6+..+1) + (6+5+..+1) + ...1

Homework Equations

The Attempt at a Solution

I know , n+(n-1)+...+1 = n(n+1)/2

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Mar 29, 2015

Svein

Science Advisor

Insights Author

So you want a formula for \frac{n(n+1)}{2}+\frac{(n-1)n}{2}+..., or \sum_{k=1}^{n}\frac{k(k+1)}{2}=\frac{1}{2}\sum_{k=1}^{n}(k(k+1))=\frac{1}{2}(\sum_{k=1}^{n}k^{2}+\sum_{k=1}^{n}k).

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