设n=1*2+2*3+3*4+……+50*51
则2n = 1*2+2*3+3*4+……+50*51
+1*2+2*3+3*4+……+50*51
=1*2+2*4+3*6+4*8+……+50*100+50*51
=2（1^2+2^2+3^2+4^2+……+50^2）+50*51
根据公式1^2+2^2+……+n^2=[(n+1)（2n+1）n]/6
则得：1^2+2^2+3^2+4^2+……+50^2=[(50+1)(2*50+1)*50]/6
=(51*101*50)/6
=（51/3）*（50/2）*101
=42925
得：2n = 2*42925+50*51=85850+2550=88400
得：n=88400/2=44200