미적분학 입문

• 카발리에리의 원리

 

 

\(S=\frac{1}{2}bh\)

\(1+2+\cdots+n = \frac{n(n+1)}{2}\)

 

 

[/pages/2696052/attachments/2084321 pyramid.gif]

 

\(V= \tfrac{1}{3}Bh\)\(V= \tfrac{1}{3}Ah\)

\(1^2 + 2^2 + 3^2 + \cdots + n^2 = {n(n+1)(2n+1) \over 6} = {2n^3 + 3n^2 + n \over 6}\)