If `0oo) (2a^n+b^n)^(1/n)=`

If 0 lt a lt b, " then " lim_(n to oo) (a^(n)+b^(n))/(a^(n)-b^(n))

lim_(n rarr oo)(a^(n)+b^(n))/(a^(n)-b^(n)), where a

lim_ (n rarr oo) ((a-1 + b ^ ((1) / (n))) / (a)) ^ (n)

If 0 lt a< b then Lt_(x to oo) (a^(n+3)+b^(n+3))/(a^(n)+b^(n))=

sum_(n=0)^( oo) (-1)^(n) x^( n+1)=

lim_(n rarr oo)((a^(n+1)+b^(n+1))/(a^(n)-b^(n))), 0 lt a lt b

If x = sum_(n=0)^(oo) a^(n) .,y=sum_(n=0)^(oo) b^(n) , z = sum_(n=0)^(oo) (ab)^(n) , where a,blt 1 , then :

lim_ (n rarr oo) n ^ (2) (x ^ ((1) / (n)) - x ^ ((1) / (n + 1))), x> 0

If x Sigma_(n=0)^(oo) (-1)^n " tan "^(2n) " and " y = Sigma_(n=0)^(oo) " cos "^(2n) theta for 0 lt theta lt pi/4 , then :