[ Toán 11 ] Tính tổng

L

lovelycat_handoi95

Ta có

[tex] \blue{(1+x)^n=C^0_n+C^1_nx+C^2_nx^2+...+C^n_n x^n[/tex]


[tex]\blue{\Leftrightarrow (1+x)^n.x^3=C^0_nx^3+C^1_nx^4+C^2_nx^5+...+C^n_n x^{n-1}(1)\\\Leftrightarrow 6x(x+1)^n+3n(1+x)^{n-1}.x^2+n[3x^2(1+x)^{n-1}+(n-1)(1+x)^{n-2}.x^3]= 2.3C^0_nx+3.4C^1_nx^2+4.5C^2_nx^3+........+(n+2)(n+3)C^n_n.x^{n+1}(2)\\\Rightarrow S = 6.2^n+3n.2^{n-1}+3n2^{n-1}+(n-1).2^{n-2}.n[/tex]


(2) Đạo hàm 2 lần hàm (1)
p/s : gõ kiểu này k quen
 
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