Question

Giúp mình vs . Mình cám ơn nhiều

A=(1/4×9+1/9×14+1/14×19+...+1/44×49)×(1-3-5-7-...-49)/89

Answer 1

\(\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right).\dfrac{1-3-5-7-...-49}{89}\)

\(=\dfrac{1}{5}.\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{19}+...+\dfrac{1}{44}-\dfrac{1}{99}\right).\dfrac{1-\left(3+5+...+49\right)}{89}\)

\(=\dfrac{1}{5}.\left(\dfrac{1}{4}-\dfrac{1}{49}\right).\dfrac{1-\dfrac{\left(3+49\right).\left[\left(49-3:2+1\right)\right]}{2}}{89}\)

\(=\dfrac{1}{5}.\dfrac{45}{196}.\dfrac{1-\dfrac{52.24}{2}}{89}\)

\(=\dfrac{9}{196}.\dfrac{1-\dfrac{1248}{2}}{89}\)

\(=\dfrac{9}{196}.\dfrac{1-624}{89}\)

\(=\dfrac{9}{196}.\left(-\dfrac{623}{89}\right)\)

\(=-\dfrac{9}{28}\)