Calculating the Sum of a Series with Sigma Notation

[xLaser]

7
----
\
/ 1 <- *note: the 1 should be more to the right.
----
N=3


Ok, this might be dumb , but it think the answer for this is 1 but I'm just making sure.

cuz i know that for example if it is

7
----
\
/ N <- *note: the N should be more to the right.
----
N=3

the answer would be 3+4+5+6+7

but if it is just a 1 there, then is it just 1? i mean the N doesn't really matter because N isn't present as a variable on the right side.

Thx guy,

Mike.

 

[Gokul43201]

Actually, the answer is not 1.

Here, try this : find

$$\sum_{N=3}^7 (N+1)$$
and use the fact that this should be equal to $$\sum_{N=3}^7 N + \sum_{N=3}^7 1$$.

From this you can find the last term, which is the one you want.

 

[xLaser]

wouldn't that be :

(3+4+5+6+7)+(1) ??

because

7
----
\
/ 1 <- *note: the 1 should be more to the right.
----
N=3

is = to 1 no matter what since there is no variable there?@@#%?!

 

[Gokul43201]

When N=3, what is (N+1) = ? And what about when N= 4 ? ...

 

[xLaser]

ok i get your question above, but how about if it is
7
----
\
/ 1 <- *note: the 1 should be more to the right.
----
N=3

by itself? this sigma by itself would just mean 1 rite?

 

[xLaser]

and it doesn't have to be limited to 1 only, what about if it is 2 there, or 3, or 4..? There is no variable N there so the N shouldn't really do anything... for any value of N the value would still be the number on the right?! doesn't that make sense?

 

[xLaser]

ooooooooooooooooooooooooooooooooooooooook i just figured it out.

for

7
----
\
/ 1 <- *note: the 1 should be more to the right.
----
N=3

it actually means t1 + t2 + t3 + t4

where t1 = 1, t2 =1 and so on,

therefore, the answer should be

1+1+1+1 = 4 !

is that rite Gokul43201

 

[shmoe]

It's not 4 either, but you're closer.

Let $$t_i=1$$ for all values of i. Your sum is

$$\sum_{i=3}^{7}t_i=t_3+t_4+t_5+t_6+t_7$$

Note that you had missed a term when you rewrote it as t1+t2+t3+t4. There are actually 5, not 4, terms in this sum. If you are going to change the index variables starting point, make sure you adjust the end carefully as well.

 

[xLaser]

aah ok thanks a lot m8.