Evaluate: (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100)

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We have to find (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100).

Now (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100).

=> [(10 - 1)/10][(11 - 1)/11][(12 - 1)/12]...[(99-1)/99][(100-1)/100].

=> (9/10)(10/11)(12/11)...(98/99)(99/100)

We see that all terms get cancelled except 9/100.

(The entire section contains 2 answers and 97 words.)

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