Question

vă rog frumos, dau coroana!​

Answer 1

Răspuns:

98285

Explicație pas cu pas:

$\displaystyle \sum_{k=1}^{13} k\cdot 2^{k-1} = 1\cdot 2^0 + 2\cdot 2^1 + 3\cdpt 2^2 + 4\cdot 2^3 + 5\cdot 2^4 + 6\cdot 2^5 + \cdots + 13\cdot 2^{12}\\ \\ = 1 + 2 + 3\cdot 4 + 4\cdot 8 + 5\cdot 16 + 6\cdot 32 + 7\cdot 64 + 8\cdot 128 + 9\cdot 256 + 10\cdot 512 + 11\cdot 1024 + 12\cdot 2048 + 13\cdot 4096\\ \\ = 1 + 2 + 12 + 32 + 80 + 192 + 448 + 1024 + 2286 + 5120 + 11264 + 24576 + 53248\\ \\ = 98285$