Question

1+3+3^2+3^3+3^4+3^5+3^6+…+3^2015

Answer 1

Explicație pas cu pas:

$(1 + {3}^{1} + {3}^{2} + ... + {3}^{2015}) \times (3 - 1) = \\ 3 + {3}^{2} + {3}^{3} + ... + {3}^{2015} + {3}^{2016} - \\ - 1 - 3 - {3}^{2} - {3}^{3} - ... - {3}^{2015} = \\ {3}^{2016} - 1 \\ \\ \\ rezulta \: ca \: suma \: ta \: este \\ \frac{ {3}^{2016} - 1 }{3 - 1} = \frac{ {3}^{2016} - 1}{2}$