Question

Caucule os seguintes produtos: a) (1-1/2).(1-1/3).(1-1/5).............. (1-1/100) b) (1+1/2).(1+1/3).(1+1/4).............(1+1/200)

Answer 1

a)

P=(1-1/2).(1-1/3).(1-1/4)...(1-1/100)

P=(2-1)/2.(3-1)/3.(4-1)/4...(100-1)/100

P=[(2-1)(3-1)(4-1)...(100-1)] / [2*3*4...*100]

P=[1*2*3*4...99] / [2*3*4...*100]

P=1 / 100

 

b)

P=(1+1/2).(1+1/3).(1+1/4)...(1+1/200)

P=(2+1)/2.(3+1)/3.(4+1)/4...(200+1)/200

P=[(2+1)(3+1)(4+1)...(200+1)] / [2*3*4...200]

P=[3*4*5...201] / [2*3*4...200]

P=[201] / [2]

P=201/2

P=100,5

 

Answer 2

Resposta:

a)

P=(1-1/2).(1-1/3).(1-1/4)...(1-1/100)

P=(2-1)/2.(3-1)/3.(4-1)/4...(100-1)/100

P=[(2-1)(3-1)(4-1)...(100-1)] / [2*3*4...*100]

P=[1*2*3*4...99] / [2*3*4...*100]

P=1 / 100

 

b)

P=(1+1/2).(1+1/3).(1+1/4)...(1+1/200)

P=(2+1)/2.(3+1)/3.(4+1)/4...(200+1)/200

P=[(2+1)(3+1)(4+1)...(200+1)] / [2*3*4...200]

P=[3*4*5...201] / [2*3*4...200]

P=[201] / [2]

P=201/2

Explicação passo a passo: