\(\displaystyle \sum_{i=k}^{n}f(i) = \sum_{i=k+p}^{n+p}f(i-p)~~~~We~change~~ i~~
from~the~initial~~k~~to~~(k+p)~~ \)

\(\displaystyle and~~~final~~from~~n~~to~~(n+p)~~while~ in~the~function~~(i-p)~~replaces~~i.\)

\(\displaystyle ~~~~~~ p~ is~any~ +tive~ or~- tive~ integer.\)

\(\displaystyle Summation~can~be~split~as~follows:- \sum_{i=k}^{n}f(i) = \sum_{i=k}^{r}f(i)+ \sum_{i=r+1}^{n}f(i) \)

.

## Comments

There are no comments in this discussion.