(x+1) + (x+2) + ... + (x+100) = 5750
(x+x+...+x) + (1+2+..+100) = 5750
100x + (101 x 100 : 2 ) = 5750
100x + 5050 = 5750
=> 100x = 5750 - 5050
100 x = 700
=> x = 700 : 100
=> x = 7
\(a.\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
\(\left(x+x+x+...+x\right)+\left(1+2+3+4+...+100\right)=5750\)
\(100x+\left(1+2+3+4+...+100\right)=5750\)
\(100x+5050=5750\)
\(100x=5750-5050\)
\(100x=700\)
\(x=700:100\)
\(x=7\)
\(b.C=2+2^2+2^3+...+2^{100}\)
\(2C=2.\left(2+2^2+2^3+2^4+...+2^{100}\right)\)
\(2C=2^2+2^3+2^4+2^5+...+2^{101}\)
\(2C-C=2^{101}-2\)
\(=>C=2^{101}-2\)
\(2^{2x-1}-2=C\)
\(2^{2x-1}-2=2^{101}-2\)
\(2^{2x-1}=2^{101}\)
\(=>2x-1=101\)
\(2x=101+1\)
\(2x=102\)
\(x=102:2\)
\(x=51\)
a) (x+1) + (x+2) +....+ (x+100) = 5750
=> ( x + x + x + ... + x ) + ( 1+ 2 + 3 + ... + 100 ) = 5750
=> 100x + (101 . 100 : 2 ) = 5750
=> 100x + 5050 = 5750
=> 100x = 5750 - 5050
=> 100x = 700
=> x = 700 : 100
=> x = 7