Question

Find the exact value of [log_e 1] + [log_e 2] + [log_e 3] + ... + [log_e 66]

Answer 1

We have 

[log₂ 1] + [log₂ 2] + [log₂ 3] + ... + [log₂ 64] 

= [log₂ 1] + [log₂ 2] + ... + [log₂ 4] + [log₂ 5] + [log₂ 6] + ... + [log₂ 8] + [log₂ 9] + [log₂ 10] + ... + [log₂ 16] + [log₂ 17] + [log₂ 18] + ... + [log₂ 32] + [log₂ 33] + [log₂ 34] + ... [log₂ 64] + [log₂ 65] + [log₂ + 66] 

= 2.3 + 3.4 + 4.16 + 5.32 + 6.2 

= 6 + 12 + 64 + 160 + 12