Simplify completely (your answer may contain n): (1-(1/3))(1-(1/4))(1-(1/5))(1-(1/6))...(1-(1/n))?

Question

Don't remember how to do this type of problem and pre-calc was so long ago for me.

(1-(1/5))(1-(1/6))...(1-(1/n))

This was cut off from the question...

Answer 1

Try simplifying it and you will see that the answer is indeed 2/n.

1- 1/3 = 2/3
1-1/4= 3/4 etc

so you get (2/3)(3/4)(4/5)....(n -2/n-1)(n-1/n)

You can divide out the matching numerators and denominators. This leaves you with the 2 from the first term and the n in the numerator from the last term.

Your answer is 2/n.

Answer 2

2/n

Answer 3

got me.

I know this: As n-->infinity, the value --> 0.

Answer 4

good luck with this one budy