1/(2×1001)+1/(3×1001)-1/(4×1001)+1/(6×1001)-1/(8×1001)

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1/(2×1001)+1/(3×1001)-1/(4×1001)+1/(6×1001)-1/(8×1001)
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1/(2×1001)+1/(3×1001)-1/(4×1001)+1/(6×1001)-1/(8×1001)
1/(2×1001)+1/(3×1001)-1/(4×1001)+1/(6×1001)-1/(8×1001)

1/(2×1001)+1/(3×1001)-1/(4×1001)+1/(6×1001)-1/(8×1001)
原式=(1/1001)*[(1/2)+(1/3)-(1/4)+(1/6)-(1/8)]
=(1/1001)*{[(1/2)+(1/3)+(1/6)]-[(1/4)+(1/8)]}
=(1/1001)*[1-(3/8)]
=(1/1001)*(5/8)
=5/8008