Math Is Fun Forum

sitaram

Guest

natural numbers.

∑ (2l+1)=n²;   here l takes on the values from l=0 , 1, 2,...........n-1.

             i've seen that it was written as

             (2n+1)= n+ 2(sum of natural numbers)...

how can we replace l with n in the summation..????

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: natural numbers.

Are you thinking of:

which can be rearranged to give:

or how to prove that those are true?

To prove it in the second form (Since that's the one you showed in your post)

Last edited by luca-deltodesco (2009-02-26 00:43:07)

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sitaram

Guest

Re: natural numbers.

it is not  "i" in the summation. it is "L"
∑ (2L+1) = ∑ (2n+1) = n+(sum of natural numbers)= n+2 {n(n-1)/2}=n² .  this is wat iam looking for.. how 2L+1 written as 2n+1.

LampShade

Member

Registered: 2009-02-22

Posts: 23

Re: natural numbers.

The letter you pick for your index variable doesn't matter.  Sometimes j or k is used instead of i.  But your line ∑ (2L+1) = ∑ (2n+1) = n² is incorrect.

The variable n represents the the largest number you are summing to (from 0 to n, perhaps).  The i is just a place holder to let you know how far along your summation you are.

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