1/2 +1/(2+4) +1/(2+4+6) +1/(2+4+6+8)…….+1/(2+4+6+8+…….解题思路

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1/2 +1/(2+4) +1/(2+4+6) +1/(2+4+6+8)…….+1/(2+4+6+8+…….
解题思路

1/2 +1/(2+4) +1/(2+4+6) +1/(2+4+6+8)+…….+1/(2+4+6+8+…….+100) =1/(1×2 )+1/(2×3) +1/(3×4) +1/(4×5)+…….+1/(50×51) =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+….+1/50-1/51 =1-1/51 =50/51