2x3+3x4+4x5+......+100x101=?

1*2+2*3+3*4+.+100*101 =1/3*1*2*3+1/3[2*3*4-1*2*3]+1/3[3*4*5-2*3*4]+.+1/3[100*101*102-99*100*101] =1/3[1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+...+100*101*102-99*100*101] =1/3*100*101*102 =343400-2=343498