Sigma Notation

Arithmetic and Geometric progressions.

Sigma Notation

Postby Guest » Tue Jan 12, 2021 3:20 am

Capture.PNG
Capture.PNG (8.11 KiB) Viewed 993 times


Is my answer on this problem acceptable?
Guest
 

Re: Sigma Notation

Postby Guest » Tue May 04, 2021 4:48 pm

I wouldn't accept it. You state that [tex]a_1^3+ a_2^3+ a_3^3+ \cdot\cdot\cdot+ a_n^3[/tex] is not equal to [tex](a_1+ a_2+ a_3+ \cdot\cdot\cdot+ a_n)^3[/tex] but you haven't shown it.
Guest
 

Re: Sigma Notation

Postby Guest » Mon Jun 07, 2021 7:44 am

By the way- whatever proof you give will have to account for the fact that what you are trying to prove is NOT always true! If n= 1 and [tex]a_1= 1[/tex] then [tex]\sum_{i= 0}^n a_i= 1[/tex] and [tex]\sum_{i= 0}^n a_i^2= 1= 1^2[/tex].
Guest
 

Re: Sigma Notation

Postby Guest » Wed Jun 23, 2021 4:15 pm

Is the problem to show that equality is not always true or that it is never true?

If it is to show that it is never true then you have the problem that, as already said, that it IS true when n= 1.

If it is to show that it is not always true then it is sufficient to show that for n= 1, [tex]a_1= a_2= 2[/tex], [tex]\sum_{i=0}^n a_i= 2+ 2= 4[/tex] while [tex]\sum_{i=0}^n i^3= 8+ 8= 16\ne 4^3[/tex],
Guest
 


Return to Progressions, Series



Who is online

Users browsing this forum: No registered users and 2 guests