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If the three consecutive coefficients in the expansion of (1+x)^n are 28, 56, and 70, then the value of n is.
解析 If n is NOT a Positive Integer(1+x)^n=1+nx+ (n(n-1))((1)(2))x^2+ (n(n-1)(n-1))((1)(2)(3))x^3+⋯ if |x|<1.This series is an infinite series, which can only be used when |x|<1, i.e. 1 x<+1....
解析 【解析】 $$ ( 1 + x ) ^ { n } = \begin{pmatrix} n \\ 0 \end{pmatrix} + \begin{pmatrix} n \\ 1 \end{pmatrix} x + \begin{pmatrix} n \\ 2 \end{pmatrix} x ^ { 2 } + \begin{pmatrix} n \\ 3 \end{pmatrix} x ^ { 3 } + .s $$ ...
The 1/N expansion of the Nakano-Schwinger functions (NSF) corresponding to the EuclideanN-componentg蠒 4 theory is performed in the framework of the static ultralocal model (SULM). The results are compared, for small value of the coupling constantg, with those obtained by means of the ...
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A Taylor series of a function f (x) around a value a is given by (Eq. 4.1)f(x)=f(a)+11!df(a)dx(x−a)1+12!d2f(a)dx2(x−a)2+13!d3f(a)dx3(x−a)3+⋯=∑n=0∞1n!dnf(a)dxn(x−a)n (Eq. 4.2)=∑n=0nmax1n!dnf(a)dxn(x−a)n+On,max Obviously, the ...