Consider a sequenced where nth term tn =(n/n+2) , n = 1 , 2 , 3 , 4 ,.......the value of t2*t3*t4*t5.........*t199 equals :

The product of the terms t2 through t199 can be written as (2/4) * (3/5) * (4/6) * ... * (199/201) by substituting n into the given formula n/(n+2). The numerators form the sequence 2, 3, 4, ..., 199, and the denominators form the sequence 4, 5, 6, ..., 201, resulting in telescoping cancellation of all intermediate terms. After cancellation, only 2 * 3 in the numerator remains, leaving 6 divided by the last two denominators, 200 and 201. This calculates to 6 / (200 * 201), which equals 6 / 40200, and simplifying this fraction gives 1/6700.

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