expansion of x 1 2 1 x 1 2 1 x 2 1 8x 2 1 16x 3 5 128x 4 According to binomial series 1 a n 1 na n n 1 2 a 2 n n 1 n 2 3 a 3 n n 1 n 2 n 3 4 a 4
In the binomial expansion formula for 1 x n 1 nx n n 1 2 x 2 substitute x for x and 1 2 for n The result would be 1 1 2 x 1 2 3 2 x 2 2 1 1 2 x 3 8 x 2 5 16 x 3 Get the free Binomial Expansion Calculator widget for your website blog Wordpress Blogger or iGoogle Find more Mathematics widgets in Wolfram Alpha
expansion of x 1 2
expansion of x 1 2
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Taylor Series Formula
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9 5 The Binomial Theorem
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Wolfram Alpha is a great tool for computing series expansions of functions Explore the relations between functions and their series expansions and enhance your mathematical knowledge using Wolfram Alpha s series expansion calculator Learn more about Expanding x y n yields the sum of the 2 n products of the form e 1 e 2 e n where each e i is x or y Rearranging factors shows that each product equals x n k y k for some k between 0 and n
This binomial expansion formula gives the expansion of 1 x n where n is a rational number This expansion has an infinite number of terms 1 x n 1 n x n n 1 2 x 2 n n 1 n 2 3 x 3 Note To apply this formula the value of x should be less than 1 The expansion of this expression has 5 1 6 terms So the two middle terms are the third and the fourth terms Use the formula
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The binomial expansion can be used to find accurate approximations of expressions raised to high powers In Pure Year 1 you learnt how to expand where n is a positive integer and being any constants We will now learn how to expand a greater range of expressions A series expansion is a representation of a particular function as a sum of powers in one of its variables or by a sum of powers of another usually elementary function f x Here are series expansions some Maclaurin some Laurent and some Puiseux for a number of common functions 1 1 x 1 x x 2 x 3 x 4 x 5 for 1
The procedure to use the binomial expansion calculator is as follows Step 1 Enter a binomial term and the power value in the respective input field Step 2 Now click the button Expand to get the expansion Step 3 Finally the binomial expansion will be displayed in the new window f x 1 2x 3x 2 4x 3 5x 4 nx n 1 Explanation We could alternatively derive a MacLaurin Series by using the Binomial Expansion The binomial series tell us that
CBSE Class 11 Maths Notes Binomial Theorem And Mathematical Induction
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Find The Middle Term In The Expansion Of x 1 6y 10 Brainly in
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expansion of x 1 2 - If n 1 x x 1 P F where P is a positive integer and 0 F 1 then P 1 th term is numerically the greatest term in the expansion of 1 x n Illustration Find the numerically greatest term in 1 3x 10 when x 1 2