Question

tìm tích

a, ( 1 phần 2 + 1 ) nhan ( 1 phần 3 + 1 ) nhàn ( 1 phần 4 + 1 ) ... (1 phan 999 + 1 )

b, ( 1 phần 2 - 1 ) nhàn (1 phần 3 - 1 ) nhàn ( 1 phần 4 - 1 ) ... ( 1 phần 1000 - 1 )

c, 3 phần 2 mũ 2 nhân 8 phần 2 mũ 2 nhận 15 phần 4 mũ 2 ... 99 phan 10 mu 2

Answer 1

a, \(\left(\dfrac{1}{2}+1\right).\left(\dfrac{1}{3}+1\right).\left(\dfrac{1}{4}+1\right)...\left(\dfrac{1}{999}+1\right)\)

\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}...\dfrac{1000}{999}\)

\(=\dfrac{3.4.5...1000}{2.3.4...999}\)

\(=\dfrac{1000}{2}\)\(=500\)

Answer 2

b, \(\left(\dfrac{1}{2}-1\right).\left(\dfrac{1}{3}-1\right).\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{1000}-1\right)\)

\(=\dfrac{-1}{2}.\dfrac{-2}{3}.\dfrac{-3}{4}...\dfrac{-999}{1000}\)

\(=\dfrac{\left(-1\right).\left(-2\right).\left(-3\right)...\left(-999\right)}{2.3.4...1000}\)

\(=\dfrac{-1}{1000}\)