Question

Consider a sequence where the nth term, tn=n/(n+2) ,
n = 1,2,3,... The value of t3xt4xt5x.......xt53 equals:​

Answer 1

Given :  a sequence where the nth term, tn=n/(n+2)

To find :   The value of t3xt4xt5x.......xt53

Solution:

tn = n/(n + 2)

t3  = 3/5

t4 = 4/6

t5  = 5/7

t52 = 52/54

t53  = 53/55

t3xt4xt5x.......xt53  =  ( 3 * 4 * ...................* 52*53)/(5 * 6 *......................* 54 *55)

= (3 * 4)/(54 * 55)

= 4/(18 * 55)

= 2/(9 * 55)

= 2/ 495

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