Sum from 1 to infinity of (cos1)^x Does this one converge?
S summergrl New member Joined Feb 21, 2007 Messages 33 Apr 4, 2007 #1 Sum from 1 to infinity of (cos1)^x Does this one converge?
pka Elite Member Joined Jan 29, 2005 Messages 11,995 Apr 4, 2007 #2 The series ∑k=1∞xk\displaystyle \sum\limits_{k = 1}^\infty {x^k }k=1∑∞xk converges if and only if ∣x∣<1\displaystyle \left| x \right| < 1∣x∣<1. We know that cos(1)≈0.54\displaystyle \cos (1) \approx 0.54cos(1)≈0.54 so does the series converge?
The series ∑k=1∞xk\displaystyle \sum\limits_{k = 1}^\infty {x^k }k=1∑∞xk converges if and only if ∣x∣<1\displaystyle \left| x \right| < 1∣x∣<1. We know that cos(1)≈0.54\displaystyle \cos (1) \approx 0.54cos(1)≈0.54 so does the series converge?
S summergrl New member Joined Feb 21, 2007 Messages 33 Apr 4, 2007 #3 yes! To find the sum I do 1/(1-cos1) which is about 2.17 correct?
skeeter Elite Member Joined Dec 15, 2005 Messages 3,218 Apr 4, 2007 #4 summergrl said: yes! To find the sum I do 1/(1-cos1) which is about 2.17 correct? no, the sum will be S = cos(1)/[1 - cos(1)] ... 1.175 Click to expand...
summergrl said: yes! To find the sum I do 1/(1-cos1) which is about 2.17 correct? no, the sum will be S = cos(1)/[1 - cos(1)] ... 1.175 Click to expand...
