Question

Sigma notation
I have this http://puu.sh/qEJh
and I want to solve it with the calculator, how do I do that?

Answer 1

I tried to type in sum(seq(sqrt(x+1)-sqrt(x),x,0,2012))
And it gives an error like Invalid Dim

Answer 2

use telescopic method.

Answer 3

the answer will be \( \sqrt{2013} \)

Answer 4

The answer's sqrt(2012) and I just learned the sigma notation so I'm not so familiar with the telescopic method >.>

Answer 5

\( S_0 = \sqrt{1} - 0\)
\( S_1 = \sqrt{1+1} - \sqrt{1} + \sqrt{1} = \sqrt{2}\)
\( S_2 = \sqrt{2+1} -\sqrt{2} + \sqrt{2} - \sqrt{1} +\sqrt{1} = \sqrt{3}\)
\( S_4 = \sqrt{4+1} - \sqrt{3} + \sqrt{2+1} -\sqrt{2} + \sqrt{2} - \sqrt{1} +\sqrt{1} = \sqrt{4}\)
...
so on

Answer 6

Sorry, it was S4 was supposed to be S3 and first term was supposed to be sqrt(3+1)

Answer 7

Why is there a +sqrt(1)? (talking about the S1)
The equation is sqrt(n+1)-sqrt(n) D:

Answer 8

@zepp Are you sure the answer is sqrt(2012)? I am also getting sqrt(2013) and check: http://www.wolframalpha.com/input/?i=sum+n+%3D+0+to+2012+%28sqrt%28n%2B1%29+-+sqrt%28n%29%29

Answer 9

Yes I'm sure it's sqrt(2012), I found out that I had the wrong upper bound of summation, it should be 2011, thank you very much guys! :D

Answer 10

you are welcome