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Ding Xiaoqing's Mathematical Analysis
It is proved that: 1)∫{ an} is strictly monotonically decreasing and converges to 0.

∴a 1>; Aortic second sound & gtAn & gt (n+1) > 0.

A(n+ 1) -An=[a 1+a2+....+a(n+ 1)]/(n+ 1)-[a 1+a2+....+an/n

= a(n+ 1)/(n+ 1)+[ 1/(n+ 1)- 1/n][a 1+a2+]....+an]

& lta(n+ 1)/(n+ 1)-n * an/[n(n+ 1)]=[a(n+ 1)-an]/(n+ 1)& lt; 0

∴a(n+ 1)& lt; One; one

That is to say, the sequence {An} is strictly monotonically decreasing.

2)∫{ an} is strictly monotonically decreasing and converges to 0.

∴ For any positive real number Q, there is m, when n >; Male, male

As long as it is proved that n exists, when n> is n, an

AN=(a 1+a2+....+aN)/N

=[a 1+a2+...+a(M- 1)]/N+[aM+a(M+ 1).....+aN/N

& lt(M- 1)* a 1/N+(N-M+ 1)* q/2/N & lt; q

To solve the above inequality, if

N> (2a1-q) (m-1)/q when an < q

That is, {An} converges to 0.

3) This problem can be proved in the same way, but it is not a monotonically decreasing sequence.