I would like study the convergence of the following sequence: u <mrow class="MJX-TeXAto

virpsojolh8ih

virpsojolh8ih

Answered question

2022-06-01

I would like study the convergence of the following sequence:
u n = ( a + 1 ) ( a + 2 ) . . . ( a + n ) n ! n

Answer & Explanation

Jaylah Washington

Jaylah Washington

Beginner2022-06-02Added 2 answers

Since log ( 1 + x ) x and k = 1 n 1 k log n ,
ln ( u n ) = 1 n k = 1 n log ( 1 + a k ) a n k = 1 n 1 k 0
thus u n 1.

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