Question

determinati x din proportiile: 1+2+3+...+25/×=1+2+2la puterea 2 +....+2la puterea 9/5115

Answer 1

[tex]\it 1+2+3+\ ...\ +25 = \dfrac{25\cdot26}{2} = 25\cdot13 = 325 \\ \\ 1+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9= \\ \\ = 1+2+4+8+16+32+64+128+256+512 = 1023 [/tex]

Proporția devine:

$\it \dfrac{325}{x} = \dfrac{\ \ 1023^{(1023}}{5115} \Rightarrow \dfrac{325}{x} =\dfrac{1}{5} \Rightarrow x = 325\cdot5$