篮球场木地板安装视频:1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)……=?

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1/2+1/4+1/8+1/16+……+1/(2的a次方)=?
共两题

1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3)……
=2/a(a+2)+1/(a+2)(a+3)+......
=3/a(a+3)+1/(a+3)(a+4)+......
=...
=n/a(a+n)

1/2+1/4+1/8+1/16+……+1/(2的a次方)
=(2^a-1)/2^a

1/a(a+1)+1/(a+1)(a+2)+…+1/(a+n)(a+n+1)
=[1/a -1/(a+1)]+[1/(a+1)-1/(a+2)]+…+[1/(a+n)-1/(a+n+1)]

=1/a -1/(a+n+1)

1/2+1/4+1/8+1/16+……+1/(2的a次方)等比数列,利用公式

=[1/2 -(1/2)*(1/2^a)]/(1-1/2)
=1- (1/2^a)

2^a表示2的a次方

1/2+1/4+1/8+1/16+……+1/(2的a次方)=1-1/(2的a次方)

这么简单啊‘
拆开分母就可以了