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

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

(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

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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