Question

Find the limit of this partial sum.

Answer 1

Or just find the sum...

Answer 2

do you recognize it as something that you might have learned prior to this?

Answer 3

are the terms in a geometric or arithmatc sequence?

Answer 4

It seems to be arithmetic

Answer 5

hm not quite; define arithmetic sequence for me

Answer 6

When you add a recurring number to the sequence?

Answer 7

Geometric is add you add a number that is multiplied

Answer 8

yep

consider this: what do we call a short cut to adding up a bunch of the same value?

say 3+3+3+3+...+3, for 15, 3s

Answer 9

3n

Answer 10

good, so multiplication

now the sum of 15 3s us just:\[\sum_{n=1}^{15}3n\]
now what do we call the shorcu version of multiplying the same value over and over again?

3*3*3*3*...*3 ; for 15, 3s

Answer 11

geometric

Answer 12

its a 'power of' , an exponent: 3^(15)

\[\sum_{n=1}^{15}3^n\]

and yes its geometric; now which of these summations matches your setup better?

3n or 3^n?

Answer 13

3^n :)

Answer 14

Ohh I see now.

Answer 15

then out sequence is geometric :)

do you recall a formula for a geo seq summation by chance?

Answer 16

Yes a/(1-r)

Answer 17

and as long as |r| < 1 itll converge to a value yes

Answer 18

Wow, it is 10. That was so simple!

Answer 19

Thank you, this makes a lot more sense now

Answer 20

:) yep