Thread: Sum of finite series

1. 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

2. 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.

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

3. didnt quite get how u are taking 17! as denominator?

and the answer cannot be 1. There is no such option

4. 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: $\frac{2}{10854718875}$ ....

5. 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?