Question

Write the sum using summation notation, assuming the suggested pattern continues.

8 + 27 + 64 + 125 + ... + n3

Answer 1

so tell me - what is the first n ?

Answer 2

we know that the first n will be 2 since 2^3 = 8
so the summation start with n =2 and goes to infinity and we sum for n^3 :

\[\sum_{n=2}^{\infty} n^3\]

Answer 3

so as you can see at the bottom we write the index n and its initial value 2
at the top we write the final value for n which is infinity in our case since it wont end (continues)
inside the summation notation we write the expression - in our case n^3

Answer 4

so you just plug the number into the n^3?

Answer 5

i hope it answers the question

Answer 6

Yes i understand thank you! How would you do one that doesn't have an "n" like
-1 + 2 + 5 + 8 + ... + 44 <<< this one

Answer 7

so we need to come up with a formula that will make our sequence

you see that the difference between two elements is 3
so we can write something like :

-1 + 3n

and start from n=0
you can see now that when n=0 we get -1
and when n=1 we get 2
etc..
we will sum to the n that will give us 44 (what n is it ?)

Answer 8

15??

Answer 9

and did you get the -1 in the equation just because its the first one in the sequence?

Answer 10

15 - correct

Answer 11

and for the -1 :
we could write the formula
-4 + 3n
as well
and start with n=1 instead of n=0 (and end with n =16 instead of our 15)

Answer 12

we could as well write
2+3n
and start with n=-1 and end with n =14

Answer 13

but it is easier to start with n=0 and have the first term in the sequence in your formula

Answer 14

ok thank you soooo much! (:

Answer 15

yw :)