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Infinite number mathematics
In advanced mathematics, what methods are there to find the limit of infinite sequence?

For example:

1: When n approaches infinity, [1/N2+1(n+1) 2+1/(n+2) 2+...+1.

2. When n approaches infinity, [1(N2+pie)+1(N2+pie)+...+1(N2+pie).

3:lim sinx (n approaches 0) limit, it is better to list the calculation steps of this limit.

I know the answers to the above three questions, but I don't know the calculation process. I don't know how the answer came from.

The limit of the problem sinx (when x approaches 0).

Best answer

1、0 & lt 1/n^2 < 1/n * 1/(n+ 1)= 1/n- 1/(n+ 1)

2、n( 1/n^2)= 1/n & gt; 1/(n 2+ faction)+1(n 2+2 faction) +...+ 1/(n 2+n faction) > 0

Pinch theorem (pinch theorem)

3. What's your question?

3. sinx = 0 when x = 0, and then it can be obtained from the continuity of sinx.

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