已知1²+2²+3²+…+n²=n(n+1)(2n+1)/6,试求:50²+51²+52²+…+101²越快回答越好...帮我一个忙.
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![已知1²+2²+3²+…+n²=n(n+1)(2n+1)/6,试求:50²+51²+52²+…+101²越快回答越好...帮我一个忙.](/uploads/image/z/32776-16-6.jpg?t=%E5%B7%B2%E7%9F%A51%26%23178%3B%2B2%26%23178%3B%2B3%26%23178%3B%2B%E2%80%A6%2Bn%26%23178%3B%3Dn%28n%2B1%29%282n%2B1%29%2F6%2C%E8%AF%95%E6%B1%82%EF%BC%9A50%26%23178%3B%2B51%26%23178%3B%2B52%26%23178%3B%2B%E2%80%A6%2B101%26%23178%3B%E8%B6%8A%E5%BF%AB%E5%9B%9E%E7%AD%94%E8%B6%8A%E5%A5%BD...%E5%B8%AE%E6%88%91%E4%B8%80%E4%B8%AA%E5%BF%99.)
已知1²+2²+3²+…+n²=n(n+1)(2n+1)/6,试求:50²+51²+52²+…+101²越快回答越好...帮我一个忙.
已知1²+2²+3²+…+n²=n(n+1)(2n+1)/6,试求:50²+51²+52²+…+101²
越快回答越好...帮我一个忙.
已知1²+2²+3²+…+n²=n(n+1)(2n+1)/6,试求:50²+51²+52²+…+101²越快回答越好...帮我一个忙.
50²+51²+52²+…+101²
=(1²+2²+3²+…+101²)-(1²+2²+3²+…+49²)
=101(101+1)(2*101+1)/6 -49(49+1)(2*49+1)/6
=101*102*203/6 -49*50*99/6
=308126
带入就行了
1²+2²+3²+…+n²=n(n+1)(2n+1)/6
S50=1²+2²+3²+…+50²=50(50+1)(2*50+1)/6=25*17*101
S101=1²+2²+3²+…+101²=101(101+1)(2*101+1)/6=101*17*203
全部展开
1²+2²+3²+…+n²=n(n+1)(2n+1)/6
S50=1²+2²+3²+…+50²=50(50+1)(2*50+1)/6=25*17*101
S101=1²+2²+3²+…+101²=101(101+1)(2*101+1)/6=101*17*203
50²+51²+52²+…+101²=S101-S50=101*17*203-25*17*101=178*17*101=305626
收起
101*(101+1)(101*2+1)÷6-49(49+1)(49*2+1)÷6=308126