natasha.aries
HEY PLEASE HELP ME! :)
Find the first four terms in the expansion of (x^1/2+1)^30
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RadEn
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use this :
30C0 (x^1/2)^30(1)^0 + 30C1 (x^1/2)^(30-1) (1)^1 +
30C2 (x^1/2)^(30-2) (1)^2 + 30C3 (x^1/2)^(30-3) (1)^3
calculate and simplify it
natasha.aries
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wait im confused do you think you can write it out on paper and attach it? im sorry and i understand if you cannot.
RadEn
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do know about combination ?
natasha.aries
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oh wait! i think i get it! but do i go all the way to thirty? thats whats confusing me?
natasha.aries
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no...:/
RadEn
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the general formula of combination is
|dw:1365545267017:dw|
do u know about factorial :)
natasha.aries
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oh wait! i do know about it loll what would be n and what would be r?
RadEn
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actually, n and r are natural number
natasha.aries
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so how would i use the formula?
RadEn
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well, first u have to know about factorial
defined n! = n*(n-1)*(n-2)*... 3 . 2. 1
an example : 4! = 4 . 3 . 2 . 1 = 24
so far so good ?
natasha.aries
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yes!
RadEn
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ah, as extra info defined 0! = 1
nah, let's going to combination above
30C0 = 30!/(30-0)!0! = 30!/30!*1 = 30!/30! = 1, right ?
natasha.aries
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yes!
RadEn
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so, what is the 30C1 ? :)
try
natasha.aries
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30
RadEn
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cool :)
natasha.aries
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do i go all the way down until i get to 1?
RadEn
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so, so on u can calculation of 30C2 and 30C3 right
natasha.aries
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yeah
RadEn
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ok, now we have the other problem about exponent
natasha.aries
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ok
RadEn
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look, that i wrote expression about 1^0, 1^1, 1^2, 1^3. these are be 1 right ? and whatever if multiplied by 1 be its self, right ?
natasha.aries
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yess
RadEn
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so, u can miss them
RadEn
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then for simplify of (x^1/2)^30, u can use the property of exponent :
(a^m)^n = a^(m*n)
so, (x^1/2)^30 = x^16, right ?
RadEn
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opp, x^15 i mean :)
natasha.aries
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yes
RadEn
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then so on, u have to simplify about
(x^(1/2))^(30-1) = (x^(1/2))^(29) = x^(29/2) = sqrt(x^29)
or u can modif again be sqrt(x^28 * x) = sqrt(x^28) sqrt(x) =
(x^(28/2)) * sqrt(x) = x^14 * sqrt(x)
RadEn
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it just simplification in radical form to exponential form
RadEn
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or just one expression sqrt(x^29) only
RadEn
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now, what about u with (x^1/2)^(30-2) (1)^2 = ... ?
natasha.aries
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ohh!! okay i understand! thank you very much!!!!
RadEn
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you're welcome
natasha.aries
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:)