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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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