If first term of a series #T_1# is #1# and #T_n=nT_(n-1)#, find the formula for #n^(th)# of the series?

1 Answer
Oct 4, 2017

#n^(th)# term is #n!#

Explanation:

Observe #2^(nd)# term #T_2# is #2# times first term #T_1# i.e. #T_2=2xxT_1#

#3^(rd)# term #T_3# is #3# times second term #T_2# i.e. #T_3=3xx2xxT_1#

#4^(th)# term #T_4# is #4# times third term #T_3# i.e. #T_4=4xx3xx2xxT_1#

and so on

Hence #n^(th)# term #T_n# is #n# times #(n-1)^(th)# term #T_(n-1)# i.e. #T_n=nxx(n-1)xx.......4xx3xx2xxT_1#

or #T_n=nxx(n-1)xx.......4xx3xx2xxT_1=n!T_1#

As here #T_1=1#, #n^(th)# term is #n!#