Question

Tìm x 2^x+1+ 2^x + 2 + 2^ x + 3 +.......+2^ x + 100 =32. (2^ 101-2)

Answer 1

Đặt A=\(2^{x+1}+2^{x+2}+...+2^{x+100}\)

=>\(2\cdot A=2^{x+2}+2^{x+3}+...+2^{x+101}\)

=>\(A=2^{x+101}-2^{x+1}\)

\(A=32\left(2^{101}-2\right)=2^{106}-2^6\)

=>\(2^{x+1}\left(2^{100}-1\right)=2^6\left(2^{100}-1\right)\)

=>x+1=6

=>x=5