\(\frac{1}{2}\)+ \(\frac{1}{4}\) + \(\frac{1}{8}\) + \(\frac{1}{16}\) + \(\frac{1}{32}\)
= [ 1 - \(\frac{1}{2}\)] + [ \(\frac{1}{2}\) - \(\frac{1}{4}\)] + [ \(\frac{1}{4}\) - \(\frac{1}{8}\)] + [ \(\frac{1}{8}\) - \(\frac{1}{16}\)] + [ \(\frac{1}{16}\) - \(\frac{1}{32}\)]
Xóa bỏ các phân số trùng lặp , ta được tổng của dãy số là :
1 - \(\frac{1}{32}\) = \(\frac{31}{32}\)
Đ/S :\(\frac{31}{32}\)
Ta thấy :
1/2 + 1/4 = 3/4 = 1 - 1/4
1/2 + 1/4 + 1/8 = 7/8 = 1- 1/8
.............................
1/2 + 1/4 + ... + 1/32 = 1 - 1/32 = 31/32
Vậy 1/2 + 1/4 + 1/8 +1/16 + 1/32 = 31/32
1/2+1/4+1/8+1/16+1/32
= (1/2+1/4+1/8+1/16+1/32)x2-(1/2+1/4+1/8+1/16+1/32)
= 1+1/2+1/4+1/8+1/16-1/2+1/4+1/8+1/16-1/32
= 1+1/2-1/2+1/4-1/4+1/8-1/8+1/16-1/16-1/32
= 1 -1/32
= 31/32.
Ủng hộ nhé.