Question

Aratati ca nr A=1-1/2+1/4-1/8+1/16-1/32 este mai mare decat 1/2

Answer 1

A=1/1-1/2+1/4-1/8+1/16-1/32

A=2/2-1/2+1/4-1/8+1/16-1/32

A=1/2+1/4-1/8+1/16-1/32

A=2/4+1/4-1/8+1/16-1/32

A=3/4-1/8+1/16-1/32

A=6/8-1/8+1/16-1/32

A=5/8+1/16-1/32

A=10/16+1/16-1/32

A=11/16-1/32

A=22/32-1/32

A=21/32

1/2 = 16/32

21/32 > 16/32 (pt ca ai numaratorul mai mare si numitorul =)

deci A > 1/2

Answer 2

A = 1-1/2+1/4-1/8+1/16-1/32 |•2

2A = 2-1+1/2-1/4+1/8-1/16

2A-2 = -1+1/2-1/4+1/8-1/16 |+1/32

2A-2+1/32 = -1+1/2-1/4+1/8-1/16+1/32

2A+1/32 - 2 = -A

3A = 2-1/32

3A = 63/32

=> A = 63/(3•32)

=> A = 63/96

63/96 > 1/2 <=> 63/96 > 48/96

=> A > 1/2