1/3 × 2/5+1/5 2/7+1/7 2/9+……1/99 × 2/101

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1/3×2/5+1/52/7+1/72/9+……1/99×2/1011/3×2/5+1/52/7+1/72/9+……1/99×2/1011/3×2/5+1/52/7+1/72/9+……1/99×2/1

1/3 × 2/5+1/5 2/7+1/7 2/9+……1/99 × 2/101
1/3 × 2/5+1/5 2/7+1/7 2/9+……1/99 × 2/101

1/3 × 2/5+1/5 2/7+1/7 2/9+……1/99 × 2/101
1/3 × 2/5+1/5 ×2/7+1/7 ×2/9+……1/99 × 2/101
=1/3-1/5+1/5-1/7+1/7-1/9+.+1/99-1/101
=1-1/101
=100/101