1, when n is odd: that is, when n = 2m- 1, an = 1/2.

2. When n is even, that is, when n = 2m, an = m = n/2.

Application of calculation:

1. Astronomical research institutions need computers to analyze space pulses and star position motions.

2. Biologists need computers to simulate protein's protein folding process and discover the mystery of genome.

Pharmacists want to develop drugs to treat cancer or various bacteria and viruses, and medical scientists are developing new methods to prevent aging.

Mathematicians hope to calculate the largest prime number and more accurate value of π.

Economists should use computer to analyze and calculate the development direction of an enterprise/city/country under the consideration of tens of thousands of factors, so as to carry out macro-control.

6. Industry needs to accurately calculate the best scheme of material, energy, processing and time allocation in the production process.

It can be seen that the future science of mankind is inseparable from calculation all the time.