唐渠铖:x/1*2+x/2*3......x/2002*2003=2002 求X

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有积分哈,要1步1步打清楚!

x/(1*2) = x(1/1 - 1/2)
x/(2*3) = x(1/2 - 1/3)
x/(3*4) = x(1/3 - 1/4)
.....
x/(2002*2003) = x(1/2002 - 1/2003)

原式 = x(1 - 1/2003) = 2002/2003*x = 2002
x = 2003

裂项法来做。

/(1*2) = x(1/1 - 1/2)
x/(2*3) = x(1/2 - 1/3)
x/(3*4) = x(1/3 - ¼)
.....
x/(2002*2003) = x(1/2002 - 1/2003)

原式 = x(1 - 1/2003) = 2002/2003*x = 2002
x = 2003

1

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