you want to actually solve this problem, then try writing a formula for the apparent nth term
i try but i can't write a formula
(it isn't hard if you know even a tiny amount of algebra)
not only tiny i'm very good in algebra
If not, I've said all I need to say.
i follow everything you say still can't write a formula
i think to see a a pattern and to invent formula base on that is a very high skill i don't have

my skills in algebra help me solve many difficult questions yet i'm lost in this one
if first term is
21 i can think of a formula
2nn
second and third terms will give me idea to correct my mistake and discover the
nth term as
(n+1)!n
which is like going back to square
1
for the sum it's very diffcult to write the
nth sum
i can't see a relation between
21 and
65 which also between
65 and
2423
the difference between numbers don't help
the division between numbers don't help
the square root between numbers don't help
the only thing i can see the denomator can work with factorial but that don't help because the original summation is also factorial
so the formula for the
nth partial some is something like
(1+n)!∗
the star* represent the relationship between all numators which is unknow for now
