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binomial expansion question?
find the first four terms in the binomial expansion of : (1+2x)^1/2
have trouble with the surd! thanks in advance!
4 Answers
- 1 decade agoFavorite Answer
Binomial expansion:
(1+p)^n = 1 + n/1!*p + {n(n-1)/2!} p^2 + {n(n-1)(n-2)/3!}p^3+...
(1 + 2x)^½ = 1 + (½)/1!(2x) + {½ (½ - 1)/2!} (2x)² + {½ (½ - 1) (½ - 2)/3!)(2x)³ + ...
Simplify ->
(1 + 2x)^½ = = 1 + x - ½ x² + ½x³+...
Also see Maclaurin series expansion too.
Source(s): http://library.thinkquest.org/C0110248/algebra/bie... http://en.wikipedia.org/wiki/Taylor_expansion - ignoramusLv 71 decade ago
I count two terms in (1 + 2x), so the people who think it is not a binomial must have trouble counting.
The procedure is exactly the same as for an integral index.
(1 + 2x)^½ = 1 + ½(2x) + {½ (½ - 1)/1.2} (2x)² + {½ (½ - 1) (½ - 2)/1.2.3)(2x)³ + .......
= 1 + x - ½ x² + ½x³ - ⅝ x^4 + .......
- 1 decade ago
sorry this is not a binomial expansion equation
