If sequence a n </msub> &gt; 0 is decreasing to 0 and <munderover> &#x2211

Davion Harding

Davion Harding

Answered question

2022-06-09

If sequence a n > 0 is decreasing to 0 and k = 1 a n = , prove n = 1 a n e S n <

Answer & Explanation

timmeraared

timmeraared

Beginner2022-06-10Added 22 answers

The only condition needed is that a n > 0 and then n 1 a n e S n 1 since with S 0 = 0 < S 1 < S 2 < . . . one has
e S n S n 1 S n e x d x a n , n 1
Then n = 1 N a n e S n 0 S N e x d x 1

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