Show that Summation x=0 to n=(n+1)_C_1 u_0+(n+1)_C_2∆ u_0+(n+1)_C_3∆^2 u_0+...+∆^nu_0 and hence

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MATH A to Z

MATH A to Z

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∆^kf(x)=Summation i=0 to k(-1)^i(k_C_i)f[x+(k-i)h] Or ∆^ky_0=Summation i=0 to k(-1)^i(k_C_i)y_(k-i)
18:46
∆^kf(x)=Summation i=0 to k(-1)^i(k_C_i)f[x+(k-i)h] Or ∆^ky_0=Summation i=0 to k(-1)^i(k_C_i)y_(k-i)
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