S=1+i−1−i+1+...
(1/i)=−i
S=i(−i+1+i−1−i+1+...)
S=i(−i+S)
S=1+iS
S(1−i)=1
∴ S=(1/(1−i))
a) Is this correct?
b) Do there exist any other sequences
in the form of:
S=(a_1 +...+a_n )+(a_1 +...+a_n )+...
S=(a_1 +...+a_n )(1+1+...+1_(m times) )
⇒S=Σ_(i=1) ^(m→∞) Σ_(j=1) ^n a_j
where a_(t+1) =ba_t , a_1 =ba_n
I′m very interested in these sequences
The general solution of equation
tan x tan 4x = 1 is
(1) (2n + 1)(π/(10)) , n ∈ Z − {n : n = 5k +2; k ∈ Z}
(2) (4n − 1)(π/(10)) , n ∈ Z
(3) ((nπ)/(10)) , n ∈ Z
(4) 2nπ + (π/(10)) , n ∈ Z