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1/24+1/60+1/120+1/210+1/336+1/504+1/720......+1/79801楼以解但不简便
题目详情
1/24+1/60+1/120+1/210+1/336+1/504+1/720......+1/7980
1楼以解
但不简便
1楼以解
但不简便
▼优质解答
答案和解析
= 1/2*3*4 + 1/3*4*5+ ...+ 1/19*20*21
=1/2 * ((4-2)/2*3*4 +(5-3)/3*4*5 +...+ (21-19)/19*20*21 )
=1/2*(1/2*3 - 1/3*4 +1/3*4 -1/4*5 + ...+1/19*20-1/20*21 )
=1/2 *(1/6 - 1/420)
=1/2* 69/420 = 23/280
=1/2 * ((4-2)/2*3*4 +(5-3)/3*4*5 +...+ (21-19)/19*20*21 )
=1/2*(1/2*3 - 1/3*4 +1/3*4 -1/4*5 + ...+1/19*20-1/20*21 )
=1/2 *(1/6 - 1/420)
=1/2* 69/420 = 23/280
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