1/(1×2×3)+1/(2×3×4)+1/(4×5×6)、、、、+1/(48×49×50)
题目
1/(1×2×3)+1/(2×3×4)+1/(4×5×6)、、、、+1/(48×49×50)
答案
1/(1×2×3)+1/(2×3×4)+1/(4×5×6)、、、、+1/(48×49×50)= 1/2 *[(3-1)/(1*2*3)+(4-2)/(2*3*4).+(50-48)/(48*49*50)]
=1/2 * [1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4).+1/(48*49)-1/(49*50)]
=1/2*(1/2-1/2450)=306/1225
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