goyalsau wrote:{ 1 / (1 * 2 * 3 * 4) } + { 1 / ( 2 * 3 * 4 * 5 ) } + { 1 / 3 * 4 * 5 * 6 ) } .......... { 1 / ( 20 * 21 * 22 * 23 ) }


IN This series , The question was to find the sum of all the series..

There may be some problem with the question. The sum can be determined if the series is considered up to infinity. In case of finite summation may be we cannot determine it. Let's see what we can do with the series.

As shovan85 said, the series can be written as (0!/4! + 1!/5! + 2!/6! + 3!/7! + ... + 19!/23!)

General n-th term of the series is given by (n - 1)!/(n + 3)!
According to the question, we have to find the sum from n = 1 to n = 20.

Now, there is a summation formula for infinite factorials,


If the question had asked for summation of the series up to infinity, we would've proceeded as follows,


But this holds only if the summation is done for infinite series.