I will post a challenging math problem each day. The level of difficulty will vary, but most problems should not require any specialized knowledge beyond calculus. Problems are also posted on Twitter using the hashtag #mathpotd.
The answer is 101/200(3/4)(8/9)(15/16)...(9999/10000)= (1-1/4)(1-1/9)(1-1/16)...(1-1/10000)= (1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/100)(1+1/100)= (1/2)(3/2)(2/3)(4/3)(3/4)...(100/99)(99/100)(101/100)= (1/2)(101/100)= 101/200
The answer is 101/200
ReplyDelete(3/4)(8/9)(15/16)...(9999/10000)
= (1-1/4)(1-1/9)(1-1/16)...(1-1/10000)
= (1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/100)(1+1/100)
= (1/2)(3/2)(2/3)(4/3)(3/4)...(100/99)(99/100)(101/100)
= (1/2)(101/100)
= 101/200