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I feel stupid...

pull it apart and make it...

(1+1/n)*(1+1/n)*(1+1/n)

do the first 2:

1 + 2/n + 1/n^2

then multiply by the last (1+1/n) each one at a time...

1 + 2/n + 1/n^2 + 1/n + 2/n^2 + 1/n^3

re-arranging them from highest to lowest power:

1/n^3 + 3/n^2 + 3/n + 1



whenever you encounter something like this (x+y)^n, you will always have n+1 terms in your answer.

i.e. this problem had (...)^3 and we had 4 terms. a "regular" foil such as (...)^2 yields 3 terms.
 
Originally posted by: cepher2101
wow...i need all the AT junkies to do my math homework...
Click to expand...

i am usually pretty anti-help with homework on the forum but it was late and i was feeling generous.
 
Probably won't check back, but, for raising binomials to larger powers than 3, check in a textbook for the binomial expansion theorem. Or, what's perhaps even a little quicker (sometimes) is using Pascal's triangle. (I'll attempt to type it here, but it's too hard to format the spacing)

...................1
.................1..1
...............1..2..1
.............1..3..3..1
...........1..4..6..4..1
.........1..5.10.10.5..1
.......1..6.15.20.15.6..1

continue the pattern, adding adjacent numbers to create the number below them.
These are the coefficients when you expand a binomial
so, (x+y)^6 would be
1x^6 + 6 x^5y + 15 x^4y^2 + 20x^3y^3 +15x^2y^4 + 6xy^5 + 1y^6
now, for a binomial other than (x+y)^n, simply replace "x" with whatever the first term is and replace y with whatever the 2nd term is.
Generally, this is slower for squared or cubed binomials, but can save time when expanding a binomial to the 4th or greater power.
 
Originally posted by: DrPizza
Probably won't check back, but, for raising binomials to larger powers than 3, check in a textbook for the binomial expansion theorem. Or, what's perhaps even a little quicker (sometimes) is using Pascal's triangle. (I'll attempt to type it here, but it's too hard to format the spacing)

...................1
.................1..1
...............1..2..1
.............1..3..3..1
...........1..4..6..4..1
.........1..5.10.10.5..1
.......1..6.15.20.15.6..1

continue the pattern, adding adjacent numbers to create the number below them.
These are the coefficients when you expand a binomial
so, (x+y)^6 would be
1x^6 + 6 x^5y + 15 x^4y^2 + 20x^3y^3 +15x^2y^4 + 6xy^5 + 1y^6
now, for a binomial other than (x+y)^n, simply replace "x" with whatever the first term is and replace y with whatever the 2nd term is.
Generally, this is slower for squared or cubed binomials, but can save time when expanding a binomial to the 4th or greater power.
Click to expand...



thats awesome...thanks man.
 
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