为了求1+2+2²+2³+...+2²º¹²的值,可令S=1+2+2²+2³+…+2²º¹²,则 2S=2+2²+³+...+2²º¹³,因此 2S-S=2²º¹³-1,所以1+2+2²+2³+...+2
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 02:09:11
![为了求1+2+2²+2³+...+2²º¹²的值,可令S=1+2+2²+2³+…+2²º¹²,则 2S=2+2²+³+...+2²º¹³,因此 2S-S=2²º¹³-1,所以1+2+2²+2³+...+2](/uploads/image/z/1024581-21-1.jpg?t=%E4%B8%BA%E4%BA%86%E6%B1%821%2B2%2B2%26%23178%3B%2B2%26%23179%3B%2B...%2B2%26%23178%3B%26%23186%3B%26%23185%3B%26%23178%3B%E7%9A%84%E5%80%BC%2C%E5%8F%AF%E4%BB%A4S%3D1%2B2%2B2%26%23178%3B%2B2%26%23179%3B%2B%E2%80%A6%2B2%26%23178%3B%26%23186%3B%26%23185%3B%26%23178%3B%2C%E5%88%99+2S%3D2%2B2%26%23178%3B%2B%26%23179%3B%2B...%2B2%26%23178%3B%26%23186%3B%26%23185%3B%26%23179%3B%2C%E5%9B%A0%E6%AD%A4+2S-S%3D2%26%23178%3B%26%23186%3B%26%23185%3B%26%23179%3B-1%2C%E6%89%80%E4%BB%A51%2B2%2B2%26%23178%3B%2B2%26%23179%3B%2B...%2B2%26%23)
为了求1+2+2²+2³+...+2²º¹²的值,可令S=1+2+2²+2³+…+2²º¹²,则 2S=2+2²+³+...+2²º¹³,因此 2S-S=2²º¹³-1,所以1+2+2²+2³+...+2
为了求1+2+2²+2³+...+2²º¹²的值,可令S=1+2+2²+2³+…+2²º¹²,则 2S=2+2²+³+...+2²º¹³,因此 2S-S=2²º¹³-1,所以1+2+2²+2³+...+2²º¹²=2²º¹³-1.仿照以上推理计算出1+9+9²+³+...+9²º¹²的值.
为了求1+2+2²+2³+...+2²º¹²的值,可令S=1+2+2²+2³+…+2²º¹²,则 2S=2+2²+³+...+2²º¹³,因此 2S-S=2²º¹³-1,所以1+2+2²+2³+...+2
S=1+9+9²+³+...+9²º¹²
9S=9+9²+³+...+9²º¹²+9²º¹³
9S-S=8S=9²º¹³-1
S=(9²º¹³-1)/8
为了求1+9+9²+³+...+9²º¹²的值,可令S=1+9+9²+³+...+9²º¹²,则 9S=9+9²+³+...+9²º¹³,因此 9S-S=9²º¹³-1,所以1+9+9²+³+...+9²º¹²=(9²º¹³-1.)除以8