One plus one third plus one sixth plus one tenth plus one fifteenth plus one twenty-one plus one twenty-eight plus one thirty-six What's one in forty-seven?

1+1／3+1／6+1／10+1／15+1／21+1／28+1／36+1／45
=1+2x(1/6+1/12+1/20+1/30+1/42+...+1/90)
=1+2x(1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+...+1/9x10)
=1+2x(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+...+1/9-1/10)
=1+2x(1/2-1/10)
=1+2x2/5
=1+4/5
＝9/5

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