Question
1/1*2 + 1/2*3 + 1/3*4 + . . . + 1/2000*2001 + 1/2001*2002
A. 1/2002
B. 1999/2002
C. 2001/2002
D. 1
I can do this, I want to know how to do it a faster way... thanks!!
A. 1/2002
B. 1999/2002
C. 2001/2002
D. 1
I can do this, I want to know how to do it a faster way... thanks!!
Answers
Reiny
How are you doing it?
Perhaps you are doing it the fastest way.
What is your choice of answers?
Perhaps you are doing it the fastest way.
What is your choice of answers?
Mazim
I just add all of them, but it is taking a long time!
Reiny
ok, that is not a good idea.
How about this....
let Sum(n) denote the sum of n terms,
sum(1) = 1/2
sum(2) = 1/2 + 1/6 = 4/6 = 2/3
sum(3) = 2/3 + 1/12 = 9/12 = 3/4
sum(4) = 3/4 + 1/20 = 16/20 = 4/5
notice any pattern yet ???
let's do one more
sum(5) = 4/5 + 1/30 = 25/30 = 5/6
I am very confident that
sum(n) = n/(n+1)
and since we see that there are 2001 terms
sum(2001) = 2001/2002
How about this....
let Sum(n) denote the sum of n terms,
sum(1) = 1/2
sum(2) = 1/2 + 1/6 = 4/6 = 2/3
sum(3) = 2/3 + 1/12 = 9/12 = 3/4
sum(4) = 3/4 + 1/20 = 16/20 = 4/5
notice any pattern yet ???
let's do one more
sum(5) = 4/5 + 1/30 = 25/30 = 5/6
I am very confident that
sum(n) = n/(n+1)
and since we see that there are 2001 terms
sum(2001) = 2001/2002
Mazim
Oh I get it, thanks!