Question

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

729 + 1000 + 1331 + 1728 + ... + n3

Answer 1

let's see! what number is we cubed it (or multiplied by itself 3 times) we get 729

Answer 2

Can you think of any number?

Answer 3

that is the first step! we need to find where the summation starts from

Answer 4

so?

Answer 5

or let's do something else look at the next term which is 1000
what number ( )^3=1000

Answer 6

what number give us 1000 if we cubed it?

Answer 7

this one should be easy

Answer 8

also 1331 kinda easy! no

Answer 9

Hey! engage in discussion please! otherwise i get bored talking to myslef

Answer 10

here some thing useful to do when you don't know factor of a number
so 729=3^6=9^3

Answer 11

Prime factorization is always helpful to factor big composite numbers

Answer 12

now then we have 9^3+10^3+11^3+12^3+.....+n^3
because 1000=10^3
and 1331=11^3
and you can make sure that 12^3=1728
so that's our summation
we need to go further

Answer 13

\[\large
729 + 1000 + 1331 + 1728 + ... + n^3 = \\ \large
9^3 + 10^3 + 11^3 + 12^3 +....+n^3 = \\ \large
\sum_{k = 9}^{n}k^3
\]

Answer 14

yes like @aum did
our series start from k=9 and continues to n

Answer 15

I wanted you to work this out by yourself though lol