Question

How to write this in Summation Notation :
3/2 - 5/4 +7/8 -9/16 +11/32 -13/64 ...

Answer 1

Notice that the denominator (the easy part here) is going from:

2 to (2)(2) to (2)(2)(2)

Answer 2

okk

Answer 3

As for the numerator:

3 to -[3 + (2)(1)] to +[3 + (2)(2)] to -[3 + (2)(3)]

Answer 4

So, you can use an index of starting at "1" and going on to infinity (because of the ellipses)

Answer 5

You will have a factor of "alternating sign" in the numerator which will be represented by (-1) to an increasing power.

With these hints, do you want to take a stab at it?

Answer 6

\[\sum_{n=1}^{\infty}\frac{ (-1)^{n+1}[3 +(n-1)(2)] }{ 2^{n} }\]

Answer 7

The first term is positive, so since your index starts at "1", the "n+1" will ensure a positive first term and alternating.

Answer 8

ohh it will be \[\sum_{n=1}^{\infty} (1+2^n)/(2^n) (-1)^{n+1}\]

Answer 9

The "n-1" in the second factor will give a "3" to start with. Just saw your work. Pretty close, but the (1 + 2^n) is off. Compare to what I posted for the summation.

Answer 10

A good thing about these types of problems is that they are self-correcting. Just write out the first several terms from any answer and you'll see if it works or not. You might want to write out the first 4 or five terms from the summation I wrote out for you.

Answer 11

Ah alright thanks!

Answer 12

All good now? @butterflyprincess

Answer 13

yes thnx!

Answer 14

You're welcome! Good luck in all of your studies and thx for the recognition! @butterflyprincess