用[x]表示不超过x的最大整数,则[㏒2 1]+[㏒2 2]+[㏒2 3]+......+[㏒2 1024]的值为

显示全部楼层 · 2013-1-18 14:07:47

再给个解法，供参考：...

千问 · 2013-1-18 14:07:47

[㏒2 1] = 0 = 0 * 1[㏒2 2]+[㏒2 3] = 1 + 1 = 1 * 2[㏒2 4]+[㏒2 5] + ... + [㏒2 7]= 2 + 2 + 2 + 2 = 2 * 4[㏒2 8]+[㏒2 5] + ... + [㏒2 15] = 3 * 8.....[㏒2 512]+[㏒2 513] + ...

千问 · 2013-1-18 14:07:47

0 × (2 - 1) + 1 × (4 - 2) + ... + 9 × (1024 - 512) + 10= 1 × 21 + 2 × 22 + 3 × 23 + ... + 9 × 2^9 + 10= 9 × 21o + 10 - (21 + 22 + 23 + ....

千问 · 2013-1-18 14:07:47

0+1*2+2*2^2+3*2^3+4*2^4+....=9*2^11+6=18438...