Let a_n= 10^n n ! for n=1,2,3, then the greatest value of n for which a_n is the greatest is

Step-by-step solution

Given, a_n= 10^n n ! , n=1,2,3, , here we see that when we increase the value of n like as 1,2,3, the value of a_n increases but when we reach at n=9 or 10 the value of a_n remain unchanged, i e , minor difference in after decimal places and when we cross the value n=10 ie , n=11 , then we see that the value of a_n is monotonically decreasing. Hence, a_n have its maximum value at n=9 or 10.