51²+53²+55²+.99²

51²+53²+55²+.99²
51²+53²+55²+.99²

51²+53²+55²+.99²
51²+53²+55²+.99²
=51² -52+² 53-² 54² + 55² -56² +…+99² -100² + 52 ² +54² +56² +……+100²
=(51+52)x(51-52)+(53+54)x(53-54）+(55+56)x(55-56)+……+(99+100)x(99-100)
+4x(26² +27² +28² +……+50² ）
=-(51+52+53+54+55+56+……+99+100）+4x[50x(50+1)x(50x2+1)/6-25x(25+1)x(25x2+1)/6]
=-(51+100)x50/2+4x[50x51x101/6-25x26x51/6]
=-3775+4x[42925-5525]
=-3775+4x37400
=-3775+149600
=145825

51²+53²+55²+....99²
=99(99+1)(99×2+1)÷6-50(50+1)(100+1)÷6