1/2+1/4+1/8+1/16+....+1/128
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+...+1/64-1/128
=1-1/128
=127/128
= 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 +...+1/64 - 1/128 = 1 - 1/128 = 127/128
Gọi số đó là A , ta có
A =\(\frac{1}{2}\) + \(\frac{1}{4}\) + \(\frac{1}{8}\) + \(\frac{1}{16}\)+.... +\(\frac{1}{128}\)
A = 1 - \(\frac{1}{2}\) + \(\frac{1}{2}\) - \(\frac{1}{4}\)+ \(\frac{1}{4}\) -\(\frac{1}{8}\) + \(\frac{1}{8}\) - \(\frac{1}{16}\) +....+\(\frac{1}{64}\) - \(\frac{1}{128}\)
Xóa bỏ các số trùng lặp , ta được :
A = 1- \(\frac{1}{128}\)
A = \(\frac{127}{128}\)
1/2+1/4+1/8+1/16+....+1/128
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+...+1/64-1/128
=1-1/128
=127/128