1/2 +1/4 +1/8 + 1/16 + 1/32 +1/64 +1/128
=1-1/2+1/2-1/4+1/4-1/8+...+1/64-1/128
=1-1/128
=127/128
gọi tổng đó là A ta có :
A = 1/2 + 1/4 + 1/8 +1/16 + 1/32 +1/64 + 1/128
2A= ( 1/2 * 2) + ( 1/4 * 2 ) + ( 1/8 * 2) + ( 1/16 * 2) + ( 1/32 * 2 ) + ( 1/64 * 2 ) + ( 1/128 * 2)
2A= 1+ 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64
TA LẤY 2A - 1A = 1A
A = ( 1 + 1/2 +1/4 + 1/8 + 1/16 + 1/32 + 1/64 ) - ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 )
TA THẤY 1/2 - 1/2 = 0 ; 1/4 - 1/4 = 0 ; 1/8 - 1/8 = 0 ;1/16 - 1/16 = 0 ; 1/32 - 1/32 = 0 ; 1/64- 1/64 = 0
NÊN A = 1 - 1/128 = 127/128
Gọi số cần tìm là a
A=1/2+1/4+1/8+1/16+1/32+1/64
A×2=1+1/2+1/4+1/8+1/16+1/32
A×2-A=(1+1/2+1/4+1/8+1/16+1/32)-(1/3+1/4+1/8+1/16+1/32+1/64)
A=1+1/2+1/4+1/8+1/16+1/32-1/2+1/4+1/8+1/16+1/32+1/64
A=1-1/64
A=63/64
1/2 +1/4 +1/8 + 1/16 + 1/32 +1/64 +1/128
=1-1/2+1/2-1/4+1/4-1/8+...+1/64-1/128
=1-1/128
=127/128
