ns am struggling to recognize basics together it associated to developing a closed kind expression native a summation. I understand the score at hand, yet do not recognize the process for i beg your pardon to monitor in stimulate to accomplish the goal.

You are watching: How to find closed form of summation

Find a closed form for the amount k+2k+3k+...+K^2. Prove her claim

My very first approach to be to turn it right into a recurrence relation, which did not occupational cleanly. After that I would attempt to rotate from a recurrence relation into a closed form, but I am unsuccessful in obtaining there.

Does anyone know of a strong approach for addressing such problems? Or any type of simplistic tutorials that have the right to be provided? The material I uncover online does not help, and causes additional confusion.

Thanks


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edited Apr 26 "15 in ~ 20:39
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Am_I_Helpful
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BusturdustBusturdust
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If you room interested in a general algorithm come compute sums favor these (and more facility ones) i can"t introduce the book A=B enough.

The authors have actually been so type to make the pdf openly available:

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

Enjoy!


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answered Apr 26 "15 at 19:02
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soegaardsoegaard
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No one provided the math approach, so ns am adding the mathematical approach to this AP problem.

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

Therefore, it method that there room altogether k terms with each other in the given series.

Next, as here all the consecutive terms are greater than the previous hatchet by a constant common difference,i.e., k.

So, this is an Arithmetic Progression.

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

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

n is the variety of terms in the series, a(1) is the an initial term that the series, and a(n) is the last(n th) ax of the series.

Here,fitting the terms of 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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Asad has defined a mathematical strategy in the comment to solving this.

If you room interested in a programming technique that functions for more facility expressions, then you deserve to use 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 in ~ 18:11

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Peter de RivazPeter de Rivaz
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