- #1
sara_87
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Homework Statement
Show that the following sequence converges:
xn= (sin(1)/2) + (sin(2)/2^2) + (sin(3)/2^3) +...+ (sin(n)/2^n)
Homework Equations
The Attempt at a Solution
To show that it converges, i want to show that it is a cauchy sequence (since all cauchy sequences converge).
I know that xn is cauchy if abs(xn-xm)< E for all E>0.
and the above sequence can be written as:
[tex]\sum(sink/2^k[/tex]
But i don't know how to proceed??
Any help would be very much appreciated.