What is the value of the following? (1-1...

What is the value of the following? `(1-1/2)(1-1/3)(1-1/4)...(1-1/(n-1))(1-1/n)`

A

`(1)/(2n)`

B

`(1)/(5n)`

C

`(1)/(3n)`

D

`(1)/(n)`

Verified by Experts

The correct Answer is:

D

Similar Questions

Explore conceptually related problems

What is the value of the following? (1-(1)/(2))(1-(1)/(3))(1-(1)/(4))dots(1-(1)/(n-1))(1-(1)/(n))

The value of (1-1/2)(1-1/3)(1-1/4)(1-1/5)…(1-1/n) is :

The value of (1 - 1/2) (1 - 1/3) (1 - 1/4)(1 - 1/5) ………(1 - 1/n) is :

Using the principle of mathematical induction, prove that (1-1/2)(1-1/3)(1-1/4)...(1-1/(n+1))= 1/((n+1))" for all " n in N .

In n = 10!, then what is the value of the following? (1)/(log_(2)n) +(1)/(log_(3)n) +(1)/(log_(4)n)+…..+ (1)/(log_(10)n)

Which of the following is equal to (1-(1)/(3))(1-(1)/(4))(1-(1)/(5))dots(1-(1)/(n))?

Using the principle of mathmatical induction, prove each of the following for all n in N (1+1/1)(1+1/2)(1+1/3)...(1+1/n)=(n+1) .

Prove the following by using the Principle of mathematical induction AA n in N (1-(1)/(2))(1-(1)/(3)) (1-(1)/(4))…….(1-(1)/(n+1))=(1)/(n+1)

What is the value of (1)/(log_(2)n)+(1)/(log_(3)n)+ . . .+(1)/(log_(40)n) ?

Determine the value of '?' in: ( 1- (1)/(2) ) ( 1- (1)/(3) ) ( 1- (1)/(4) ) ......... (1- ( 1)/( n) ) = ?