I am having a great deal of difficulty with this exercise.

Clues are

>irem(floor(evalf(K*10^n,N)),10) can be used to find the nth digits of the decimal expansion of K

A given process.

The following procedure P(n) counts the number of prime numbers ≤ n.
> P:=proc(n) local c,i;
c:=0; # initialize the counter c=0
for i from 1 to n do
if type(i,prime) then c:=c+1;
end if; # increase c by 1 if i is prime

I believe this is a result of my ignorance rather then the flaws of the system. Can anyone teach me how to do this question?

Given 

>sum(1/n, n = 1 .. N)

I want to find the value of N such that sum(1/n, n = 1 .. N) is greater then 20.12.

>solve(sum(1/n, n = 1 .. N) > 20.12, N)

Warning, solutions may have been lost

Help please! Thanks.

Here is what I tried.

I need to get the sum of all the real roots of 3*sin(x^2) = x

So I tried this. 

>solve(3*sin(x^2)-x = 0, x, AllSolutions)

Which gaved me this 3*sin(RootOf(_Z-9*sin(_Z)^2))

Then >sum(3*sin(RootOf(_Z-9*sin(_Z)^2)), _Z = -infinity .. infinity)

Which gives me this answer which I cannot make sense of.  signum(sin(RootOf(_Z-9*sin(_Z)^2)))*infinity