Question

How would I evaluate:
(question in picture)

Answer 1

question in picture????????

Answer 2

Hi Keroro :)

How are you dear ?

Answer 3

Its easy . It is just summation. nothing more than it.

Answer 4

Hello. I am well and you?

Answer 5

I would like to know the logic behind it when i evaluate it...

Answer 6

When n = 2, it would give 1/2
n=3, 2/3
n=4, 3/4
n=5, 4/5

Now you need the telescopic method to solve for n.

Answer 7

We notice that the denominator has the same value than n

Answer 8

Therefore this summation would give \(\large\frac{n-1}{n}\)

Answer 9

Wait are not you asking for infinite series. Then there is not actual formula to evaluate this. You have to use infinite geometric sum may be.

Answer 10

Are you saying we find a general formula for the series after substituting in values?

Answer 11

Don't you know infinite geometric sum?

Look these are infinite series. So they can't solve easily. You have to use technique. Either geometric sum or telescoping sum series. Which suits best.

I hope you are getting.

Answer 12

In fact, the value 'n' tells you when to stop adding, so the result should be:
\[\large \sum_{r=2}^{n}(\frac{1}{r-1}-\frac{1}{r})=\frac{r-1}{r}\]

Answer 13

sorry, I dont get how the fact that n tells you when to stop adding, allows you to get to the answer so quickly?

Answer 14

@zepp we can approximate its result. You have leave its result in the mid way.

Look at the question it says to evaluate.
Yes you are doing right but complete it.

Answer 15

And what does telescoping imply?