Hi, I am currently dealing with this math problem and I don't know how to transfer this calculation (shown in picture) into R.

I wish to express this as the function of N (and plot it in the graph for j=1:9)

The alpha_i(j) stands for the no. of the integers 1:i that its first digit is j.

And I have created a function: first_digit() to return the first digit of a positive integer.

The script below is so far I've done.

My goal is to try to get the result of the first summation (which should be in terms of i and N)

Then sum up for i=1:N to get the final result

The major problem is that I do not know how to incorporate two summations together.

Could anyone give me some idea? Thanks a lot!

```
repla1<-1
prob.a<-function(N){
for(i in 1:N){
v<-c(1:i)
alpha=0
for(b in 1:i){
repla1=first_digit(v[b])
alpha=alpha+1
}
k = i:N
sum(alpha/(k*N))
```