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avatar+1124 

Hi friends,

 

Trust you are all doing well...please, i really have only this last question....I have tried several things...but just do not get it...

 

Prove that ∑nk=3(2k−1)n=n3−4n

 

If I evaluate the left hand side, I end up with Tn=2n2−3n

 

So I was thinking that to prove 2n2−3n=n3−4n, I could just subtract the one from the other, and I should get 0..alas, this is not working...I am asking please for some guidance here...Thank you for your time..

 Mar 16, 2023

4+0 Answers

 #1
avatar+33660 
+1

As follows:

 

 Mar 16, 2023
 #2
avatar+1124 
0

Hi Alan,

 

Gosh, what a piece of work!!..Thank you very much indeed.

 

I follow the sum up to the point where 2j+3 changes to j+3(n−2),

 

Could I ask if you would please just explain that bit to me?...Thanks Alan...

juriemagic  Mar 16, 2023
 #3
avatar+33660 
0

I set j = k-2, so k=3 becomes j = 1, and k = n becomes j = n-2.  Then:

 

The sum Σmj=1j  is given by m(m+1)/2,  so when m = n-2, the sum is (n-2)(n-1)/2.

Alan  Mar 16, 2023
edited by Alan  Mar 16, 2023
 #4
avatar+1124 
0

Understood..thank you Alan. Stay blessed..

juriemagic  Mar 16, 2023

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