Question

2 la puterea x + 2 la puterea x+1 +....... +2 la putere x +9=4092

Answer 1

2^x + 2^(x+1) +....... +2^(x +9)=4092

S= 2^x + 2^(x+1) +....... +2^(x +9)   inmultim cu 2
2S= 2^(x+1) + 2^(x+2) +....... +2^(x +10)        
2S= 2^(x+1) + 2^(x+2) +....... +2^(x +10)   +2^x-2^x
2S=2^x+ 2^(x+1) + 2^(x+2) +....... +2^(x +10)  -2^x
2S=S+2^(x +10)  -2^x
S=2^(x +10)  -2^x

2^(x +10)  -2^x =4092
2^x ×(2^10-1)=4092
2^x ×(1024-1)=4092
2^x ×1023=4092
2^x =4092:1023
2^x =4
2^x =2^2
x=2