You are watching: How to find closed form of summation

Find a closed create for the amount k+2k+3k+...+K^2. Prove your claim

My initially technique wregarding revolve it into a recurrence relation, which did not job-related cleanly. After that I would attempt to rotate from a recurrence relation into a closed create, yet I am uneffective in gaining tright here.

Does anyone know of a solid technique for addressing such problems? Or any simplistic tutorials that have the right to be provided? The material I discover digital does not assist, and also reasons even more confusion.

Thanks

algorithm math amount series recurrence

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edited Apr 26 "15 at 20:39

Am_I_Helpful

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asked Apr 26 "15 at 17:57

BusturdustBusturdust

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## 3 Answers 3

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If you are interested in a general algorithm to compute sums prefer these (and even more complicated ones) I can not recommend the book A=B sufficient.

The authors have been so kind to make the pdf easily available:

http://www.math.upenn.edu/~wilf/AeqB.html

Enjoy!

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answered Apr 26 "15 at 19:02

soegaardsoegaard

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No one offered the mathematical approach, so I am including the mathematical technique to this AP problem.

Given series is 1k + 2k + 3k + .... + k.k(OR k^2)

Because of this, it means that tbelow are altogether k terms together in the given series.

Next, as right here all the consecutive terms are greater than the previous term by a consistent common distinction,i.e., **k**.

So, this is an Arithmetic Progression.

Now, to calculate the basic summation, the formula is offered by :-

S(n) = n/2a(1)+a(n) where,S(n) is the summation of series upto n terms

n is the number of terms in the series, a(1) is the first term of the series, and also a(n) is the last(n th) term of the series.

Here,fitting the regards to the given series into the summation formula, we acquire :-

S(n) = k/21k + k.k = (k/2)*{k+k^2) = ***<(k^2)/2 + (k^3)/2>***.

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answered Apr 26 "15 at 20:02

Am_I_HelpfulAm_I_Helpful

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Asad has explained a mathematical approach in the comments to resolving this.

If you are interested in a programming strategy that functions for more complex expressions, then you can usage Sympy in Python.

For example:

import sympyx,k = sympy.symbols("x k")print sympy.sum(x*k,(x,1,k))prints:

k*(k/2 + k**2/2)

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answered Apr 26 "15 at 18:11

Peter de RivazPeter de Rivaz

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