Pls give detailed solution and its explaination :

1) If f(x) = 1/3 { f( x+1) + 5/ f( x+2) } and f(x) 0 for all x belongs to R then lim x-- oo f(x) = ???

a) 0 b) (2/5)^1/2 c) ( 5/2 )^1/2 d) infintiy

2) If k = lim x --- oo ( E1000k =1 ( x+k)m / xm + 101000 ) and ( m 101) then k = ???

a) 10 b) 102 c) 103 d) 104

(* oo implies infinity. E implies summation running from k =1 to 1000)

1.

given: ..............(1)

taking limit on both sides:

...............(2)

therefore substitute this value in eq(2):

2.

given:

dividing the by .

therefore

thus

hope this helps you.

cheers!!

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