Giải thích các bước giải:
Đặt `A=(1+1/3).(1+1/8).(1+1/15)...............(1+1/2409)`
$⇒A= \dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}....\dfrac{2401}{2400}$
`=>A=2^2/3 . 3^2/8 .4^2 /15......49^2/2400`
$⇒A= \dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}....\dfrac{2401}{2400}$
$⇒A=\dfrac{(2.3.4...49).(2.3.4...49)}{(1.2.3...48).(3.4.5...50)}$
`=>A={49.2}/{50.1}`
`=>A={(49.2):2}/{50:2}`
`=>A=49/25`
Vậy tổng `(1+1/3).(1+1/8).(1+1/15)...............(1+1/2409)=49/25`
`#Math`
