1−3⋅14+6 (14)2−…(−1)r12(r+1)(r+2)(14)r+…=?1-3\cdot\frac{1}{4}+6\ \left(\frac{1}{4}\right)^2-\ldots\left(-1\right)^r\frac{1}{2}\left(r+1\right)\left(r+2\right)\left(\frac{1}{4}\right)^r+\ldots=? 1−3⋅41+6 (41)2−…(−1)r21(r+1)(r+2)(41)r+…=?
12564\frac{125}{64} 64125
(12)3\left(\frac{1}{2}\right)^3 (21)3
(25)−3\left(\frac{2}{5}\right)^{-3} (52)−3
64125 \frac{64}{125} 12564
(1+14)−3=(54)−3=(45)3=64125\left(1+\frac{1}{4}\right)^{-3}=\left(\frac{5}{4}\right)^{-3}=\left(\frac{4}{5}\right)^3=\frac{64}{125} (1+41)−3=(45)−3=(54)3=12564
