∴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.