递等式计算,能简算的要简算 (9+9×9+9×9×9)×0.01

问题描述:

递等式计算,能简算的要简算 (9+9×9+9×9×9)×0.01

初始值a1=9,q=9,个数为n=3
用等比数列公式Sn=a1/(1-q)-a1/(1-q)*q^n计算

(9+9×9+9×9×9)×0.01
=【9×(1+9)+9×9×9】×0.01
=【 9×(10+9×9)】×0.01
=9×99×0.01
=9×0.99
=9-0.09
=8.91