## Realated Questions

Which among 21/2, 31/3, 41/4, 61/6 and 121/12 is the largest?

- Each of the numbers x
_{1}, x_{2}, .....,x_{n}, n > 4, is equal to 1 or -1. Suppose,

x_{1}x_{2}x_{3}x_{4}+ x_{2}x_{3}x_{4}x_{5}+ x_{3}x_{4}x_{5}x_{6}+ ....... + x_{n-3}x_{n-2}x_{n-1}x_{n }+_{ }x_{n-2}x_{n-1}x_{n}x_{1 }+ x_{n-1}x_{n}x_{1}x_{2}+ x_{n}x_{1}x_{2}x_{3}= 0, then, Let D be a recurring decimal of the form, D = 0. a

_{1}a_{2}a_{1}a_{2}a_{1}a_{2}..................., where digits a_{1}and a_{2}lie between 0 and 9. Further, at most one of them is zero. Then which of the following numbers necessarily produces an integer, when multiplied by D?