Integers and fractionsHow would I write this as an integer or a fraction in lowest terms?(1−12)(1+12)(1−13)(1+13)(1−14)(1+14)…..(1−199)(1+199)I really need to understand where to start and the process if anyone can help me.

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tswe0uk · Accepted Answer

Rewrite it instead as(1−12)(1−13)⋯(1−198)(1−199)×(1+12)(1+13)⋯(1+198)(1+199}Evaluate left and right parts separately. Hint: Look at how numerator and denominator cancel.For example,(1−12)(1−13)(1−14)(1−15)=12⋅23⋅34⋅45=15.

Melissa Collins · Accepted Answer

Hint: telescopy, note how the adjacent like-colored terms all cancel out of the products below(1-12)(1-13)⋯(1-1n)&amp;nbsp;=&amp;nbsp;1223344&amp;nbsp; ⋯ &amp;nbsp;n-1n-1n&amp;nbsp;=&amp;nbsp;1n(1+12)(1+13)⋯(1+1n)&amp;nbsp;=324354&amp;nbsp;5⋯n&amp;nbsp;n+1n&amp;nbsp;=&amp;nbsp;n+12Hence∏k=2n(1−1k2)&amp;nbsp;=&amp;nbsp;n+12nFollow the above link for many more examples of telescopic proofs (additive and multiplicative).

Integers and fractions How would I write this as an integer

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