1. Tính nhanh
a) \(\frac{1995.1997-1}{1996.1995+199_{ }}\) b) \(\frac{2}{3.5}\) + \(\frac{2}{5.7}\) + \(\frac{2}{7.9}\) + \(\frac{2}{9.11}\) + ... + \(\frac{2}{13.15}\)
c ) \(\frac{2}{1.2}\) + \(\frac{2}{2.3}\) + \(\frac{2}{3.4}\) + ... + \(\frac{2}{8.9}\) + \(\frac{2}{9.10}\) d) \(\frac{1}{3}\) + \(\frac{1}{9}\) + \(\frac{1}{27}\) + ... + \(\frac{1}{729}\)
b) 2/3.5+2/5/7+2/7.9+2/9.11+...+2/13.15
=1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+..+1/13-1/15
=1/3-1/15
=4/15
c) 2/1.2+2/2.3+2/3.4+..+2/8.9+2/9.10
=2(1/1.2+1/2.3+1/3.4+..+1/8.9+1/9.10)
=2(1-1/2+1/2-1/3+1/3-1/4+..+1/8-1/9+1/9-1/10)
=2(1-1/10)
=2.9/10=9/5
d) 1/3+1/9+1/27+...+1/729
đặt A=1/3^1+1/3^2+1/3^3+..+1/3^6
3A=1+1/3+1/3^2+...+1/3^5
3A-A=1+1/3+1/3^2+...+1/3^5-1/3-1/3^2-1/3^3-...-1/3^6
2A=1-1/3^6
2A=728/729
A=728/729:2
A=364/729
