Consider the sequence defined by a1=1a_1 = 1a1=1 and an+1=an+log2(1+1n)a_{n+1} = a_n + \log_2(1 + \frac{1}{n})an+1=an+log2(1+n1). What is the value of a1024a_{1024}a1024?
101010
111111
1+log2(1023)1 + \log_2(1023)1+log2(1023)
1+log2(1024)1 + \log_2(1024)1+log2(1024)