Question

Tính nhanh: (1+1/2) + (1+1/6) + (1+1/12) + .....+(1+1/9900) + (1+1/10100)

 

Answer 1

A = 1+ 1+1+ ...+ 1 +(\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{9900}+\dfrac{1}{10100}\))

=(1+1+1+...+1)+ (\(\dfrac{1}{1x2}+\dfrac{1}{2x3}+\dfrac{1}{3x4}+...+\dfrac{1}{99x100}+\dfrac{1}{100x101}\))

=100 +\(1-\dfrac{1}{101}=100-\dfrac{100}{101}=\dfrac{10000}{101}\)

Answer 2

1+1/2+1+1/6+1+1/12+...+1+1/9900

=1+1/1*2+1+1/2.3+....+1+1/99*100

=100*1+1-1/2+1/2-1/3+1/3-1/4...+1/99-1/100

=100+99/100

=10099/100