` (1+1/(2!)+2/(3!)+(2^(2))/(4!)+(2^(2))/(5!)+...)/(1 + 1/(2!)+1/(4!)+1/(6!)+...)` is equal to

(1+1/(2!)+2/(3!)+2^2/(4!)+2^3/(5!)+.....oo)/(1+1/(2!)+1/(4!)+1/(6!)+....oo) equals

(1/(1!)+(1)/(2!)+(1)/(4!)+(1)/(6!)+…)-(1/(1/(1)+(1)/(3!)+(1)/(5!)+…)) is equal to

The sum of the infinite series (1)/(2) ((1)/(3) + (1)/(4)) - (1)/(4)((1)/(3^(2)) + (1)/(4^(2))) + (1)/(6) ((1)/(3^(3)) + (1)/(4^(3))) - ...is equal to

(1+(1)/(2!)+(1)/(4!)+(1)/(6!)+....)^(2)-(1+(1)/(3!)+(1)/(5!)+(1)/(7!)+....)^(2)=