suma directa

k·( 1 [+]...(m)...[+] 1 )^{n+1} = ...
... ( 1^{n+1} [+]...(m)...[+] 1^{n+1} ) = ...
... ( 1^{n} [+]...(m)...[+] 1^{n} )·1 = ...
... m·1 = m


( 1 +...(m)...+ 1 )^{n+1} = ...
... ( 1 +...(m)...+ 1 )^{n}·(1 +...(m)...+ 1 ) = ...
... m^{n}·m = ...
... m^{n+1}


on hem utilitzat:
( x [+] y )·z = (x·z) [+] (y·z)


k·( a [+]...(m)...[+] a )^{n+1} = ...
... ( a^{n+1} [+]...(m)...[+] a^{n+1} ) = ...
... ( a^{n} [+]...(m)...[+] a^{n} )·a = ...
... (m·a^{n})·a = m·a^{n+1}


( a +...(m)...+ a )^{n+1} = ...
... ( a +...(m)...+ a )^{n}·( a +...(m)...+ a ) = ...
... (ma)^{n}·ma = ...
... (m·a)^{n+1}


(1/2^{(n+(-1))})·( x[+]y )^{n} = x^{n}+y^{n}


(1/2)·( x[+]y )^{2} =  (1/2)·( x[+]y )·( x[+]y ) = x^{2}+y^{2}


(1/2)·( x[+]y )^{2} = ( (x+iy)·(x+(-i)y) )