Solve the limit of y n </msub> = ( 1 + 1 n 3 </msu

zato1kom7

zato1kom7

Answered question

2022-05-20

Solve the limit of y n = ( 1 + 1 n 3 ) n 2

Answer & Explanation

nicoupsqb

nicoupsqb

Beginner2022-05-21Added 5 answers

You can use the (easily to verify) fact that ( 1 + 1 m ) m < 3 for all m N as follows:
( 1 + 1 n 3 ) n 2 1 = 1 n 3 k = 0 n 2 1 ( 1 + 1 n 3 ) k 1 n 3 n 2 ( 1 + 1 n 3 ) n 2 1 1 n ( 1 + 1 n 3 ) n 3 3 n n 0

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