Question

Tính

A = ( 1 - 1/1+2 ) * ( 1 - 1/1+2+3 ) * ( 1 - 1 /1+2+3+4 ) * ........ * ( 1 -1/1+2+3+......+100 )

Answer 1

https://i.imgur.com/KHpWnuh.jpg

Answer 2

\(A=(1-\frac{1}{1}+2)\cdot\left(1-\frac{1}{1}+2+3\right)\cdot\left(1-\frac{1}{1}+2+3+4\right)\cdot....\cdot\left(1-\frac{1}{1}+2+3+...+100\right)\)

Answer 3

\(Ta\) \(có\)\(:\) \(\frac{1}{1}\left(2+1\right)\cdot\frac{1}{1}\left(1-2+3\right)\cdot\frac{1}{1}(1-2+3+4)\cdot...\cdot\frac{1}{1}(1-2+3+...+100)\)

⇒\(\frac{1}{3}\cdot\frac{1}{2}\cdot\frac{1}{6}\cdot...\cdot\frac{1}{4400}\)

⇒\(\frac{1}{3}\cdot\frac{1}{2}\cdot\frac{1}{3\cdot2}\cdot\frac{1}{11\cdot2\cdot2\cdot100}\)

⇒\(1(\frac{1}{3}\cdot\frac{1}{2}\cdot\frac{1}{3\cdot2}\cdot...\cdot\frac{1}{11\cdot2\cdot2\cdot100})\)

⇒\(1(1\cdot\frac{1}{11\cdot2\cdot2\cdot100})\)

⇒\(1\cdot\frac{1}{4400}\)

➩\(\frac{1}{4400}\)

Chúc bạn học tốt!