(1/1×2×3)+(1/2×3×4)+(1/3×4×5)+.(1/98×99×100)等于多少啊?
问题描述:
(1/1×2×3)+(1/2×3×4)+(1/3×4×5)+.(1/98×99×100)等于多少啊?
(1/1×2×3)+(1/2×3×4)+(1/3×4×5)+.(1/98×99×100)
等于多少啊?
答
原式=1/2*[2/(1*2*3)+2/(2*3*4)+...+2/(98*99*100)] =1/2*[(3-1)/(1*2*3)+(4-2)/(2*3*4)+...+(100-98)/(98*99*100)] =1/2*[3/(1*2*3)-1/(1*2*3)+4/(2*3*4)-2/(2*3*4)+...+100/(98*99*100)-98/(98*99...