Find the limit?
#a_1=1 & a_n=n(a_(n-1)+1)# for n=2,3,..... Define #P_n=(1+1/a_1)*(1+1/a_2)*................*(1+1/a_n)#
Then, having defined:
Now if we substitute the formula for
and clearly we can establish by induction that:
Remembering that the MacLaurin formula for the exponential function is:
converging for every
and conclude that: