# Sum of finite series

• April 1st 2009, 01:05 PM
champrock
Sum of finite series
What is the value of

1*2 / 3! + (2*2^2)/4! + (3*2^3)/5! ............... (15*2^15)/17!

I tried making a general term for this but was unable to proceed further with that method. Secondly I multiplied the sum by 2 and tried to subtract it from the original (AP-GP sort of a method) but that is also not taking me any further.

Please guide me on this.

Thanks
• April 1st 2009, 07:35 PM
Schung
The answer is 1.
You can first use 17! as denominator. You can then find that it is a very standard AP and GP questions.

Quote:

Originally Posted by champrock
What is the value of

1*2 / 3! + (2*2^2)/4! + (3*2^3)/5! ............... (15*2^15)/17!

I tried making a general term for this but was unable to proceed further with that method. Secondly I multiplied the sum by 2 and tried to subtract it from the original (AP-GP sort of a method) but that is also not taking me any further.

Please guide me on this.

Thanks

• April 1st 2009, 09:47 PM
champrock
didnt quite get how u are taking 17! as denominator?

and the answer cannot be 1. There is no such option :)
• April 1st 2009, 10:06 PM
mr fantastic
Quote:

Originally Posted by Schung
The answer is 1.
You can first use 17! as denominator. You can then find that it is a very standard AP and GP questions.

The answer is not quite exactly equal to 1. To paraphrase the greatest spy of all time - Missed it by this much: $\frac{2}{10854718875}$ ....
• April 1st 2009, 11:09 PM
champrock
hehe.. actually the options given are all pretty close. so , there is no way to figuring out that ways.

the correct answer is given as 1- (2^16)/17!

any way to derive this?