> Digits:=100;

Sum2N:=proc(N)
evalf(sum(n/(2^n),n=1..N));
end:

Digits := 100

> Sum2N(400);

2.0000000000000000000000000000000000000000000000000...
2.0000000000000000000000000000000000000000000000000...

> Sum2N2:=proc(N)
evalf(sum(n^2/(2^n),n=1..N));
end:

> Sum2N2(400);

6.0000000000000000000000000000000000000000000000000...
6.0000000000000000000000000000000000000000000000000...

> Sum2N3:=proc(N)
evalf(sum(n^3/(2^n),n=1..N));
end:

> Sum2N3(400);

26.000000000000000000000000000000000000000000000000...
26.000000000000000000000000000000000000000000000000...

>