Hello,

can someone prove this to me as.

Any help would help save thier hair I have not torn out as yet.

If

$\displaystyle a_n,b_n$

are sequences of real number ,n>m then:

$\displaystyle \sum_{k=m}^{n}a_k .b_k=$$\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