Question

Tìm giá trị của A=1+1/2+1/3x4+1/4x5+...+1/99x100+1/100

( Lưu ý:" / "là dấu phân số, "x" là dấu nhân)

Answer 1

A=\(1+\frac{1}{2}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{99\cdot100}+\frac{1}{100}\)

=\(\left(1+\frac{1}{2}+\frac{1}{100}\right)+\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+....+\frac{1}{99\cdot100}\right)\)

=\(\frac{151}{100}+\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{99}-\frac{1}{100}\right)\)

=\(\frac{151}{100}+\frac{1}{3}-\frac{1}{100}\)

=\(\frac{11}{6}\)