Question

summation by parts formula

Answer 1

for any two sequences \(\{a_n\}\), \(\{b_n\}\)

\[\rm \sum\limits_{n=p}^qa_nb_n = \sum\limits_{n=p}^{q-1}A_n(b_n-b_{n+1}) + A_qb_q - A_{p-1}b_p \]

where \(\rm A_n = \sum\limits_{k=0}^na_k\)

Answer 2

so ?

Answer 3

why the index of \(p\) got shifted and how do i make sense of this formula as a whole ?

Answer 4

i liked this argument about the Box