` 1 + 4^2/(3!) + 4^4/(5!) + ....... oo` =

(1.3)/(1!) +(2.4)/(2!)+(3.5)/(3!) + (4.6)/(4!) + .......oo = .......

1+ 1/(2!)+2/(3!)+4/(4!)+ .... oo =

1+ (1 + 2) / (2!) + (1 + 2 + 3) / (3!) + (1 + 2 + 3 + 4) / (4!) + ...... oo

(1+x^2/(2!) +x^4 /(4!) + .....oo)^(2) - (x+x^3/(3!) +x^(5)/(5!) + ....oo)^(2) =

1+ (1) / (2) (. 3) / (5) (1.3) / (2.4) ((3) / (5)) ^ (2) + (1.3.5) / (2.4.6) ( (3) / (5)) ^ (3) + ........ oo =