Question

2la0+2la1+2la2+......+2la10+1=

Answer 1

$2^0+2^1+2^2+...+2^n=2 ^{n+1}-1$

$2^0+2^1+2^2+...+2^{10}+1=2^{11}$

Answer 2

$2^{0} + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} +1$=

=$1+ 1 + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10}$=

=$2* 2^{0} + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10}$=

=$2^{1} + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} +1$=

=$2* 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} +1$=

=$2^{2} + 2^{2} + 2^{3} +...+ 2^{10} +1$=

=$2* 2^{2} + 2^{3} +...+ 2^{10} +1$=
..................................
=2*$2^{10}$=$2^{11}$

sau, asa cum a scris respondentul anterior, folosesti formula:

$2^{n+1} - 1= (2-1)( 2^{n} + 2^{n-1} + 2^{n-2} +.....+ 2^{1} + 2^{0} )$, adica:

$2^{11} - 1= (2-1)( 2^{10} + 2^{9} + 2^{8} +.....+ 2^{1} + 2^{0} )$ deci:

$2^{0} + 2^{1} + 2^{2} + 2^{3} +...+ 2^{10} +1$=$2^{11}$