Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Mathematics
Mathematics
Problem If the sum of the series
( 1 2 − 1 3 ) + ( 1 2 2 − 1 2 ⋅ 3 + 1 3 2 ) + ( 1 2 3 − 1 2 2 ⋅ 3 + 1 2 ⋅ 3 2 − 1 3 3 ) \left(\frac{1}{2} - \frac{1}{3}\right) + \left(\frac{1}{2^2} - \frac{1}{2 \cdot 3} + \frac{1}{3^2}\right) + \left(\frac{1}{2^3} - \frac{1}{2^2 \cdot 3} + \frac{1}{2 \cdot 3^2} - \frac{1}{3^3}\right) ( 2 1 − 3 1 ) + ( 2 2 1 − 2 ⋅ 3 1 + 3 2 1 ) + ( 2 3 1 − 2 2 ⋅ 3 1 + 2 ⋅ 3 2 1 − 3 3 1 ) + ( 1 2 4 − 1 2 3 ⋅ 3 + 1 2 2 ⋅ 3 2 − 1 2 ⋅ 3 3 + 1 3 4 ) + … + \left(\frac{1}{2^4} - \frac{1}{2^3 \cdot 3} + \frac{1}{2^2 \cdot 3^2} - \frac{1}{2 \cdot 3^3} + \frac{1}{3^4}\right) + \dots + ( 2 4 1 − 2 3 ⋅ 3 1 + 2 2 ⋅ 3 2 1 − 2 ⋅ 3 3 1 + 3 4 1 ) + … α β \frac{\alpha}{\beta} β α α \alpha α β \beta β α + 3 β \alpha + 3\beta α + 3 β Browse the problem library