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" Limit "(5^(n+1)+3^(n)-2^(2n))/(5^(n)+2...

" Limit "(5^(n+1)+3^(n)-2^(2n))/(5^(n)+2^(n)+3^(2n+3))=

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lim_(n rarr oo)(5^(n+1)+3^(n)-2^(2n))/(5^(n)+2^(n)+3^(2n+3))

lim_(nrarroo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

lim_(nrarroo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

lim_(nrarroo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

5.lim_ (n rarr oo) (2 ^ (n + 1) + 3 ^ (n + 1)) / (2 ^ (n) + 3 ^ (n)) is

lim_ (n rarr oo) (2.3 ^ (n + 1) -3.5 ^ (n + 1)) / (2.3 ^ (n) + 3.5 ^ (n)) =

Using mathematical induction, prove that (1)/(1.3.5) + (2)/(3.5.7) +….+(n)/((2n-1)( 2n+1) ( 2n+3)) =( n(n+1))/( 2(2n+1) (2n+3))

Prove that 5^(n) (1+(n)/(5) +(n(n-1))/(5*10) +(n(n-1)(n-2))/(5*10*15)+…oo)=3^(n) (1+(n)/(2)+(n(n+1))/(2*4)+(n(n+1)(n+2))/(2*4*6)+…oo)