Question

limit n tends to infinity 3.2^n+1-4.5^n+1/5.2^n+7.5^n

Answer 1

Given: $\lim_{n \to \infty}${ 3x2^(n+1) - 4x5^(n+1) } / { 5x2^n + 7x5^n }

To find: Solve the problem.

Solution:

• We have given the limit from zero to infinity.

• As we have given the terms in n+1 power, breaking it to simple form, we get:

            $\lim_{n \to \infty}$ { 3 x 2^n x 2 - 4 x 5^n x 5) } / { 5x2^n + 7x5^n }

• Now taking the similar terms together, we get:

            $\lim_{n \to \infty}$ { 6 x 2^n - 20 x 5^n } /  { 5x2^n + 7x5^n }

• Now  multiplying by 5^n in denominator of both numerator and denominator, we get:

            $\lim_{n \to \infty}$ { 6 x (2/5)^n - 20 } / { 5x(2/5)^n + 7 }

• Now applying the limits, as n tends to infinity, so2/5 ^n tends to 0.

              = -20/7

Answer:

             So the answer for this limit is -20/7.