Question

1+5+9+...+(4n-3)=n(2n-1) prin metoda inductiei
Eu fac in alt mod: P(1):1=1•(2•1-1) A
P(2):1+5 de aici cum fac???
VA ROGG AM NEVOIEE DE AJUTORR!!!!

Answer 1

1. Verificarea
P(1) 1=1•(2•1-1)=>1=1•(2-1)=>1=1•1=>1=1 A
n=1
p(2) 1+5=2×(2×2-1)=> 6=2×3=>6=6A
n=2(inlocuiesti n cu 2 apoi la P(3) cu 3, etc)
2. Pp(presupunem) P(k) adevărat
Dem ca P(k+1) adevărat
P(k)= 1+5+9+...+(4k-3)=k(2k-1)
P(k+1)= 1+5+9+...+(4(k+1)-3)=k+1(2(k+1)-1
1+5+9+...+(4(k+1)-3)=k+1(2k)
1+5+9+...+4(k)+4(k+1)-3=k+1(2k)
``````````````````````````(Tu faci o acolada)
k(La a doua)
k(La a doua)+ 4(k+1)-3=k+1(2k)

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