急 1/1*2*3+1/2*3*4+1/3*4*5+.+1/n(n+1)(n+2)的值 *是乘号
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急 1/1*2*3+1/2*3*4+1/3*4*5+.+1/n(n+1)(n+2)的值 *是乘号
an=1/[n(n+1)(n+2)]=(1/2)[1/(n(n+1)- 1/((n+1)(n+2))]
=(1/2) [1/n-1/(n+1)]-(1/2)[1/(n+1)-1/(n+2)]
an-1=(1/2)[1/(n-1)-1/n]- (1/2)[1/n-1/(n+2)]
..
a2=(1/2)[(1/2-1/3)]-(1/2)[(1/3-1/4)
a1=(1/2)[(1-1/2)-(1/2)(1/2-1/3)
a1+a2+..+an=(1/2)(1-1/n)-(1/2)(1/2-1/(n+2)
=1/4+1/(2n+4)-1/(2n)
=(1/2) [1/n-1/(n+1)]-(1/2)[1/(n+1)-1/(n+2)]
an-1=(1/2)[1/(n-1)-1/n]- (1/2)[1/n-1/(n+2)]
..
a2=(1/2)[(1/2-1/3)]-(1/2)[(1/3-1/4)
a1=(1/2)[(1-1/2)-(1/2)(1/2-1/3)
a1+a2+..+an=(1/2)(1-1/n)-(1/2)(1/2-1/(n+2)
=1/4+1/(2n+4)-1/(2n)
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