Question

Korzystając ze wzoru dwumianowego Newtona, zapisz w postaci sumy:

(x-2) do 7 potęgi.

Proszę o pomoc:)

Answer 1

( 7 nad 0 ) = 1

(7 nad 1 ) = 7

(7 nad 2 ) = [ 7 !]/ [2* 5 !] = [ 6*7]/2 = 21

(7 nad 3 ) = [ 7 ! ] / [ 3 ! * 4 ! ] = [ 5*6*7]/6 = 5*7 = 35

(7 nad 4 ) = 35

( 7 nad 5) = 21

(7 nad 6) =   7

( 7 nad 7 ) = 1

zatem

( x -2) ^7 = x^7 + 7x^6 *( -2) + 21 x^5*(-2)^2 + 35x^4 *(-2)^3 + 35 x^3*(-2)^4 + 21 x^2 *(-2)^5 + 7 x*(-2)^6 + (-2)^7 =

= x^7 + 14 x^6 + 84 x^5 - 280 x^4 + 560 x^3 - 672 x^2  + 448 x - 128

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