why do we use non-increasing instead of decreasing? When writing, one way to avoid confusing anybody is to use "strictly increasing" and "non-decreasing" or "weakly increasing", and avoid the unadorned "increasing"
The function $f (n) = (1 + 1 n) ^ {n+1}$ is decreasing The point to have a decreasing upper bound for e, in addition to an increasing lower bound for e, furnished by the sequence you mentioned One can nicely squeeze e between these two sequences re 2, overkill or not, it uses quite a bit of theory that may not be available to somebody having to solve this problem
Decreasing perpetuity problem - Mathematics Stack Exchange A perpetuity pays 1000 immediately The second payment is 97% of the first payment and is made at the end of the fourth year Each subsequent payment is 97% of the previous payment and is paid four