in the expansion of 1 x 2 m 1 x 2 n The coefficient of the x 2 term of x 1 m is m choose 2 which is the same as frac m m 1 2 Because x 2 is even the coefficient for 1 x n is frac n n 1 2
What is the expansion for 1 x n Could find only the expansion upto the power of 3 Is there some general formula IIT JEE 1999 If in the expansion of 1 x m 1 x n the coefficients of x and x2 are 3 and 6 respectively then m is equal to A 6 B 9 C 12
in the expansion of 1 x 2 m 1 x 2 n
in the expansion of 1 x 2 m 1 x 2 n
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Prove That The Term Independent Of X In The Expansion Of x 1x 2n
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Binomial Expansion With A Negative Power YouTube
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Around 1665 Isaac Newton generalized the binomial theorem to allow real exponents other than nonnegative integers The same generalization also applies to complex exponents In this generalization the finite sum is replaced by an infinite series In order to do this one needs to give meaning to binomial coefficients with an arbitrary upper index which cannot be done using the usual formula with factorials However for an arbitrary number r one can define where is the Pochhammer symbol In the expansion of 1 x m 1 x n the coefficients of x and x 2 are respectively 3 and 6 Then m equals
I m used to dealing with binomial expansion in the form 1 x n I understand that if the number is not 1 then you have to divide the whole bracket by something which would make Answer Step by step video solution for If in the expansion of 1 x m 1 x n the coefficients of x and x 2 are 3 and 6 respectively the value of m and n are by Maths
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The Greatest Coefficient In The Expansion Of 1 X 2n 2 Is
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Learn how to expand binomials to any power using the binomial theorem formula and its properties Find the binomial coefficients terms applications and solved problems with PDF notes and video lessons 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
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 Learn how to expand binomials of the form 1 x n using the binomial expansion formula See examples derivation and applications of the formula for natural and rational powers
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in the expansion of 1 x 2 m 1 x 2 n - Learn how to use the binomial theorem to expand 1 x 1 and get the answer 1 x x2 x3 x4 See the explanation the binomial series formula and the answer link