Question

So sánh:

1/56+1/57+..+1/100 và 1/1.2+1/3.4+...+1/99.100

Giup mình với nhé .Mình đang cần gấp!

Answer 1

Ta có

\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{100}\right)-2\left(\frac{1}{2}+\frac{1}{4}+....+\frac{1}{100}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{100}\right)-1-\frac{1}{2}-\frac{1}{3}-....-\frac{1}{50}\)

\(=\frac{1}{51}+\frac{1}{52}+.....+\frac{1}{100}\)

=>.....

Answer 2

Ta có

 

11.2+12.3+....+199.100=1−12+13−14+....+199−11001.21​+2.31​+....+99.1001​=1−21​+31​−41​+....+991​−1001​

=(1+12+13+....+1100)−2(12+14+....+1100)=(1+21​+31​+....+1001​)−2(21​+41​+....+1001​)

=(1+12+13+....+1100)−1−12−13−....−150=(1+21​+31​+....+1001​)−1−21​−31​−....−501​

=151+152+.....+1100=511​+521​+.....+1001​