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Abzal2001
@Abzal2001
July 2022
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ЕкарныйБабай
1³+2³+ +n³=(n(n+1)/2)²
n=1 1³=(1(1+1)/2)²=1 верно
пусть верно для n=k
дjкажем для n=k+1 1³+2³+ +(k+1)³=((k+1)(k+2)/2)²
(k(k+1)/2)²+(k+1)³=k²(k+1)²/4+(k+1)³=(k+1)²[k²/4+k+1] =(k+1)²[(k²+4k+4)/4]= (k+1)²(k+2)²/4=((k+1)(k+2)/2)² чтд
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Answers & Comments
n=1 1³=(1(1+1)/2)²=1 верно
пусть верно для n=k
дjкажем для n=k+1 1³+2³+ +(k+1)³=((k+1)(k+2)/2)²
(k(k+1)/2)²+(k+1)³=k²(k+1)²/4+(k+1)³=(k+1)²[k²/4+k+1] =(k+1)²[(k²+4k+4)/4]= (k+1)²(k+2)²/4=((k+1)(k+2)/2)² чтд