lim n→∞ (2 n+1 + 3 n+1 )/(2 n + 3 n ) is equal to (a) 2 (b)3 (c) 5 (D) none. explain pls.

lim n→∞ (2n+1 + 3n+1)/(2n + 3n) is equal to (a) 2 (b)3 (c) 5 (D) none. explain pls.

Grade:12th Pass

3 Answers

36 Points
11 years ago

2^(n+1)+3^(n+1) =3^(n+1){(2/3)^(n+1) +1}

2^n+3^n =3^n{(2/3)^n +1}

As n tends to infinity (2/3)^n tends to 0

So the required limit is 3


Chetan Mandayam Nayakar
312 Points
11 years ago

(2n+1 +3n+1)/(2n +3n)=2n+1/(2n + 3n)+3n+1/(2n + 3n)=2/(1+(3/2)n)+3/(3+(2/3)n)=0+1=1


jitender lakhanpal
62 Points
11 years ago

Dear Aditi,


correct answer is 3 as (2/3)n   where n is ∞ is 0

so if we take 3n+1  from numerator and 3n  is denominator so we get (2/3)n  form


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