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Entrance to Mathematical Puzzles
What is the smallest number of people who could have been asked the question?
2. Something = nothing?
Let S= 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + . . . . . . .
Then taking 1/2 of each term
1/2 S= 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + . . . . . . .
Subtract 1/2 S from S, the result is
1/2 S= 1/2 + 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + . . . . . . . .
Subtracting the first expression for
1/2 S from the second expression for
1/2 S, we get
1/2 + (1/3  1/4) + (1/5  1/6) + . . . . = 0
Or 1/2 + 1/12 + 1/30 + 1/56 + 1/90 = 0
Proving that something equals nothing.
Do you believe it? Or, is there a reason? Explain.
1/2 + 2/4 + 3/8 + 4/16 + 5/ 32 + . . . =
Solutions to Last Mathematical Puzzle
Entrance to Mathematical Puzzles