Can someone prove this to me

  • #1
Hello,
can someone prove this to me as.
Any help would help save my hair I have not torn out as yet.:cry:

If \(\displaystyle
a_n,b_n
\)are sequences of real number ,n>m then:

\(\displaystyle
a_{n+1}S_n-a_m S_{m-1}+\sum_{k=m}^{n}( a_k - b_{k+1})S_k
\)
Where \(\displaystyle
S_n
\)is the partial sum of sequence \(\displaystyle
\sum_{k=1}^{\infty}b_n
\)

Thanks for any help
 

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
9,395
3
the tag here is tex, not math, in the square brackets.

If [tex]
a_n,b_n
[/tex]
are sequences of real number ,n>m then:

[tex]
a_{n+1}S_n-a_m S_{m-1}+\sum_{k=m}^{n}( a_k - b_{k+1})S_k
[/tex]
Where [tex]
S_n
[/tex]is the partial sum of sequence [tex]
\sum_{k=1}^{\infty}b_n
[/tex]

nope, still makes no sense.
 
  • #3
yes that's right

thanks
 
  • #4
mathwonk
Science Advisor
Homework Helper
2020 Award
11,091
1,291
what color is your hair?
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
41,833
961
miss lollita said:
If [tex]
a_n,b_n
[/tex]
are sequences of real number ,n>m then:

[tex]
a_{n+1}S_n-a_m S_{m-1}+\sum_{k=m}^{n}( a_k - b_{k+1})S_k
[/tex]
equals what??
Where [tex]
S_n
[/tex]is the partial sum of sequence [tex]
\sum_{k=1}^{\infty}b_n
[/tex]
Presumably you mean "Where [tex]
S_n
[/tex]is the partial sum of sequence
[tex]\sum_{k=1}^n b_n[/tex]
 
  • #7
sorry

[tex]\sum_{k=1}^n (a_k . b_k)[/tex]=[tex]a_{n+1}S_n-a_m S_{m-1}+\sum_{k=m}^{n}( a_k - b_{k+1})S_k[/tex]
 
Last edited:

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