Series Question (1 Viewer)

[frenzal_dude]

Find the sum of 10 terms of the series log3 + log6 + log12 +........
gvien that log3 = 0.4771 and log2 = 0.301. (All logs are base 10).

I couldn't work this out because it doesn't seem to be an AP or a GP, because log6/log3 doesn't equal log12/log6.

 

[Trebla]

Find the sum of 10 terms of the series log3 + log6 + log12 +........
gvien that log3 = 0.4771 and log2 = 0.301. (All logs are base 10).

I couldn't work this out because it doesn't seem to be an AP or a GP, because log6/log3 doesn't equal log12/log6.

Note that:
log 3 + log 6 + log 12 + ......
= log 3 + log (3 x 2) + log (3 x 2 x 2) + .....
= log 3 + (log 3 + log 2) + (log 3 + 2log 2) + .....
This is an AP with first term log 3 and common difference log 2