求1+3+6+10+15+21+28.+4950+5050简便计算方法
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求1+3+6+10+15+21+28.+4950+5050简便计算方法
![求1+3+6+10+15+21+28.+4950+5050简便计算方法](/uploads/image/z/13628342-38-2.jpg?t=%E6%B1%821%2B3%2B6%2B10%2B15%2B21%2B28.%2B4950%2B5050%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95)
通项an =1+2+3+...+n= n(n+1)/2 = n²/ 2 + n/2
Sn= ( 1² + 2² +3² +...+n² )/2 +( 1+2+3+...+n)/2
= n(n+1)(n+2)/6
S100= 171700
Sn= ( 1² + 2² +3² +...+n² )/2 +( 1+2+3+...+n)/2
= n(n+1)(n+2)/6
S100= 171700