Some sample about infinite sum
2006-08-24 14:14
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First, let we see a infinite sum: S = 1+1/2+1/4+1/8+1/16+..... is equal to 2,beacause if we get
2S = 2+1+1/2+1/4+1/8+...=2+S => S= 2.
On the other hand,this same reasoning suggests that we ought to define T=1+2+4+8+16= -1,because
2T = 2+4+8+16+32+... = T-1 => T = -1.
Something funny is going on;how can we get a negative number by summing positive quantities?
The main reason is that S and T is different, S has the sum,but T does not.
2S = 2+1+1/2+1/4+1/8+...=2+S => S= 2.
On the other hand,this same reasoning suggests that we ought to define T=1+2+4+8+16= -1,because
2T = 2+4+8+16+32+... = T-1 => T = -1.
Something funny is going on;how can we get a negative number by summing positive quantities?
The main reason is that S and T is different, S has the sum,but T does not.
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