If G is the geometric mean of numbers 1, 2, 2², 2³,.....2^n-1, then what is the value of 1 + 2log₂G ?

If H is the harmonic mean of numbers 1, 2, 2², 2³, ......2^n-1 what is n/H equal to ? 

Consider the following statements :

1. 2 + 4 + 6 + ........ + 2n = n2 + n

2. The expression n2 + n + 41 always gives a prime number for every natural number n

Which of the above statements is/are correct ?

Let P be the sum of first n positive terms of an increasing arithmetic progression A. Let Q be the sum of first n positive terms of another increasing arithmetic progression B.

Let P ∶ Q = (5n + 4) ∶ (9n + 6)