Question

Let n = 1! + 4! + 7! +......+ 400! then tens digit of n is

Answer 1

We have
n=1! + 4!+ 7!+ 10! +13!.............+ 400!
10! and all other subsequent terms are multiple of 100 hence the last two digits will be 00.
Hence to consider ten's digit of n, 1! + 4! +7! is enough.
1!=1
4!= 4*3*2*1 =24
7=7*6*5*4*3*2*1= 5040
Now
1!+4!+7!= 1 + 24 + 5040 = 5065
hence the 10th digit will be 6.