Sn = Sum from k=1 to n of Ck*cos (kt), where Ck = 1/2^k.

Prove Sn >= .7 for 0 <= t <= .1.

This question is killing me.

Here is what I've got so far:

I estimated cos kt > .95 for 0 <= kt <= .3 which hits the first three terms... now I need to find a lower bound for all the terms, and I think (from previous examples) I'm going to have to use the difference form of the triangle inequality...? Any guidance would be greatly appreciated. Thanks.