If `a_(+a_2)+a_3++a_n=1AAa_1>0,i=1,2,3, ,n ,` then find the maximum value of `a1 2a_2a_3a_4a_5 a_ndot`

Explanation

We have
A.M. `ge` H.M
`implies ((S)/(S - a_(1)) + (S)/(S - a_(2)) + ….. + (S)/(S - a_(n)))/(n) ge (n)/((S - a_(1))/(S) + (S - a_(2))/(S) + … + (S - a_(n))/(S))`
or `(S)/(S - a_(1)) + (S)/(S - a_(2)) + …. + (S)/(S - a_(n)) ge (n^(2) S)/(nS - (a_(1) + a_(2) + ...... + a_(n)))`
or `(S)/(S - a_(1)) + (S)/(S - a_(2)) + ... + (S)/(S - a_(n)) ge (n^(2) S)/(nS - S)`
or `(S)/(S - a_(1)) + (S)/(S - a_(2)) +.........+ (S)/(S - a_(n)) ge (n^(2))/(n - 1)`