Math  /  Algebra

QuestionWrite an explicit formula for the sequence: {43,6e14+e1,7e26+e2,8e38+e3,9e410+e4,10e512+e5,}an=\begin{array}{l} \left\{\frac{4}{3}, \frac{6-e^{1}}{4+e^{1}}, \frac{7-e^{2}}{6+e^{2}}, \frac{8-e^{3}}{8+e^{3}}, \frac{9-e^{4}}{10+e^{4}}, \frac{10-e^{5}}{12+e^{5}}, \cdots\right\} \\ a_{n}= \end{array}

Studdy Solution
Combine the patterns from the numerators and denominators to write the explicit formula for the sequence:
an=n+3en12n+1+en1a_n = \frac{n + 3 - e^{n-1}}{2n + 1 + e^{n-1}}

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