数学题 求解 1+\(\frac{1}{3}\)+\(\frac{1}{3^2}\)+\(\frac{1}{3^3}\)+\(\frac{1}{3^4}\)+\(\frac{1}{3^5}\)+\(\frac{1}{3^6}\)+\(\frac{1}{3^7}\)+\(\frac{1}{3^8}\)+\(\frac{1}{3^9}\)+\(\frac{1}{3^10}\)
解题思路：
令 S =1+\(\frac{1}{3}\)+\(\frac{1}{3^2}\)+\(\frac{1}{3^3}\)+\(\frac{1}{3^4}\)+\(\frac{1}{3^5}\)+\(\frac{1}{3^6}\)+\(\frac{1}{3^7}\)+\(\frac{1}{3^8}\)+\(\frac{1}{3^9}\)+\(\frac{1}{3^10}\) 设为 等式①
那么 ，
3S=3+1+\(\frac{1}{3}\)+\(\frac{1}{3^2}\)+\(\frac{1}{3^3}\)+\(\frac{1}{3^4}\)+\(\frac{1}{3^5}\)+\(\frac{1}{3^6}\)+\(\frac{1}{3^7}\)+\(\frac{1}{3^8}\)+\(\frac{1}{3^9}\) 设为 等式②
等式②减去等式①，则：
2S = 3 – \(\frac{1}{3^10}\) ，那么：
最终答案 ： S= \({3}-\frac{1}{3^10}\over{2}\)
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