3*(1*2+2*3+3*4+4*5+5*6+...+99*100) ( ) A.98*99*100 B.99*100*
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B.99*100*101

n(n+1)=n^2+n

1^2+2^2+...+n^2

=n(n+1)(2n+1)/6

3*(1*2+2*3+3*4+4*5+5*6+...+99*100)

=3*(1^2+1+2^2+2+3^2+3+4^2+4+5^2+5+...+99^2+99)

=3*(1^2+2^2+3^2+4^2+5^2+...+99^2+1+2+3+4+5+.+99)

=3*[99*(99+1)*(2*99+1)/6+(1+99)*99/2]

=3*[99*100*199/6+100*99/2]

=99*50*199+50*99*3

=99*50*(199+3)

=99*50*202

=99*100*101