f(1)=1 f(10)=2 Now, since the number in question is v. large, we'll try to generalize. Counting the no. of 1s upto 100 1/21/31/41/51/61/71/81/91=9 and 10/11/12/13/14/15/16/17/18/19=10+1 and 1 in 100 So, f(100)=21 Now, for f(1000), for each slot of hundred we get 20 1s(excluding the hundred's digit in 100-199). And 100 1s in hundreds place So, total 1s=20*10+100+1(for 1000)=301 Now, f(10^1)=2=1*10^0+1 f(10^2)=2*10^1+1=21 f(10^3)=3*10^2+1 So, the generalization is f(10^n)=n*10^(n-1)+1 so, f(10^100)=100*10^99+1=10^101+1 Answer is C
none !!
ReplyDeletewrong try again !
ReplyDeletef(1)=1
ReplyDeletef(10)=2
Now, since the number in question is v. large, we'll try to generalize.
Counting the no. of 1s upto 100
1/21/31/41/51/61/71/81/91=9 and 10/11/12/13/14/15/16/17/18/19=10+1 and 1 in 100
So, f(100)=21
Now, for f(1000), for each slot of hundred we get 20 1s(excluding the hundred's digit in 100-199). And 100 1s in hundreds place
So, total 1s=20*10+100+1(for 1000)=301
Now, f(10^1)=2=1*10^0+1
f(10^2)=2*10^1+1=21
f(10^3)=3*10^2+1
So, the generalization is f(10^n)=n*10^(n-1)+1
so, f(10^100)=100*10^99+1=10^101+1
Answer is C
implex, is this correct?
ReplyDelete