1x2十2x3十3x4十…...十1o0x101

Question

1x2十2x3十3x4十…...十1o0x101

Answer 1

应用公式
1+2+3+.+n=1/2*n(n+1)
1^2+2^2+3^2+...+n^2=1/6n(n+1)(2n+1)
1x2十2x3十3x4十…...十100x101
=1x(1+1)十2x(2+1)十3x(3+1)十…...十100x(100+1)
=(1^2+2^2+3^2+.+100*2)+(1+2+3+...+100)
=1/6*100*101*201+1/2*101*100
=1/6*10100(201+3)
=10100*34
=343400