{6^(-1)+((3)/(2))^(-1)}

{6^(-1)+(frac(3)(2))^(-1)}^(-1)= ?

EXAMPLE 11. Simplify: {6^(-1)+(frac(3)(2))^(-1)}^(1)

((-1+i sqrt(3))/(2))^(6)+((-1-i sqrt(3))/(2))^(6)+((-1+i sqrt(3))/(2))^(5)+((-1-i sqrt(3))/(2))^(6)

((-1+isqrt(3))/2)^6+((-1-isqrt(3))/2)^6+((-1+isqrt(3))/2)^5+((-1-isqrt(3))/2)^5 is equal to

If S=(1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^(2)))+(1)/(6)((1)/(2^(3))+(1)/(3^(3))) then S=

Sum of the series (1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^(2)))+(1)/(6)((1)/(2^(3))+(1)/(3^(3)))-... is