Question

2/1+4/1+8/1+16/1+32/1+64/1+128/1+256/1怎样才能简便算出它们

Answer 1

2/1+4/1+8/1+16/1+32/1+64/1+128/1+256/1
=2+4+8+16+32+64+128+256
=2*(1-2^8）/(1-2)
=2^9-2
=512-2
=510
该数列是等比数列

等比数列的求和公式是a1(1-q^n)/(1-q) a1表示第一项 n表示项数 q表示公比 q=an/a(n-1)

Answer 2

2/1+4/1+8/1+16/1+32/1+64/1+128/1+256/1
=2/1+4/1+8/1+16/1+32/1+64/1+128/1+256/1+256/1-256/1
=2/1+4/1+8/1+16/1+32/1+64/1+128/1+128/1-256/1
=2/1+4/1+8/1+16/1+32/1+64/1+64/1-256/1
=……
=1-256/1
=256/255

Answer 3

2/1+4/1+8/1+16/1+32/1+64/1+128/1+256/1 =2/1+4/1+8/1+16/1+32/1+64/1+128/1+256/1+256/1-256/1 =2/1+4/1+8/1+16/1+32/1+64/1+128/1+128/1-256/1 =2/1+4/1+8/1+16/1+32/1+64/1+64/1-256/1
=2/1+4/1+8/1+16/1+32/1+32/1-256/1
=2/1+4/1+8/1+16/1+16/1-256/1
=2/1+4/1+8/1+8/1-256/1
=2/1+4/1+4/1-256/1
=2/1+2/1-256/1
=1-256/1
=256/255