Find the product of

(1-1/6)(1-1/7)(1-1/8)................(1-1/n+5) for n>=4

(a)1/n+5

(b)2/n+4

(c)5/n+5

(d)3/(n+4)(n+5)

(e)3/n+3

Ans :c

(1-1/6)(1-1/7)(1-1/8)……(1-1/(n+5))

=(6/6-1/6)(7/7-1/7)(8/8-1/8)……

((n+5)/(n+5)-1/(n+5))

=(5/6)(6/7)(7/8)……((n+4)/(n+5))

Cancel 6,7,8,……,(n+4):

=5/(n+5)