Question

\(y=\frac{\frac{4000}{1}+\frac{3999}{2}+\frac{3998}{3}+...+\frac{1}{4000}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{4001}}=?\)

Answer 1

Đặt A=\(\frac{4000}{1}+\frac{3999}{2}+\frac{3998}{3}+........+\frac{1}{4000}\)

A=\(1+\left(1+\frac{3999}{2}\right)+\left(1+\frac{3998}{3}\right)+........+\left(1+\frac{1}{4000}\right)\)

A=\(\frac{4001}{4001}+\frac{4001}{2}+\frac{4001}{3}+...........+\frac{4001}{4000}\)

A=\(4001.\left(\frac{1}{2}+\frac{1}{3}+........+\frac{1}{4000}+\frac{1}{4001}\right)\)

=>\(y=\frac{4001.\left(\frac{1}{2}+\frac{1}{3}+........+\frac{1}{4001}\right)}{\frac{1}{2}+\frac{1}{3}+.........+\frac{1}{4001}}\)

=>\(y=4001\)