If x_p = cos(pi/2^p) + is in(pi/2p ) , then what is the value of (x_1x_3x_5....to infty)+1/(x_2x_4x_6....to infty)?

Marco Hudson

Marco Hudson

Answered question

2022-08-04

If x p = cos ( π / 2 p ) + i sin ( π / 2 p ), then what is the value of ( x 1 x 3 x 5 . . . . t o   ) + 1 / ( x 2 x 4 x 6 . . . . t o   )?

Answer & Explanation

Hamza Conrad

Hamza Conrad

Beginner2022-08-05Added 20 answers

as x goes to
x 0 = 1 + o i , x 1 = i
x 2 = 2 2 + 2 2 i
x 3 = .999 + 0.00685 i
x 4 = 0.9999994 + 0.003427 i
....
x n = 1 + 0 i = 1
{ 1 , 0 , 2 2 , .99994 , .999994 , . . . . , 1 }
{ 0 , 1 , 2 2 , .0034685 , .003427 , . . . , 0 }
so as n goes to , real part goes to 1, and imaginary goes to 0

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