Can someone prove this to me

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

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

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matt grime
Homework Helper
the tag here is tex, not math, in the square brackets.

If $$a_n,b_n$$
are sequences of real number ,n>m then:

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

nope, still makes no sense.

yes that's right

thanks

mathwonk
Homework Helper
2020 Award

silver:rofl:

HallsofIvy
Homework Helper
miss lollita said:
If $$a_n,b_n$$
are sequences of real number ,n>m then:

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

sorry

$$\sum_{k=1}^n (a_k . b_k)$$=$$a_{n+1}S_n-a_m S_{m-1}+\sum_{k=m}^{n}( a_k - b_{k+1})S_k$$

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