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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
For the Recurrence relation. i was doing this steps:
an = 2n - 5n
WTS : an = 7an-1 - 10an-2
Lets prove LHS = RHS
2n - 5n = 7an-1 - 10an-2
= 7(2n-1 - 5n-1) - 10(2n-2 - 5n-2)
= 7 X 2n-1 - 7 X - 5n-1 - 10 X 2n-2 + 10 X 5n-2
= "? " from this line how can i solve this problem & prove LHS = RHS (2n - 5n = 2n - 5n )
Please answer this ques using my steps.please and solve this problem (try to show the work line by line )

Transcribed Image Text:10. Show that an = 2″ − 5″ is also a solution to the recurrence relation
an = 7an-1-10an-2. What would the initial conditions need to be for
this to be the closed formula for the sequence?
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- (a) Male honeybees are from single parent families; they are from unfertilized eggs so only have mothers. Female honeybees are from two parent families; they are from fertilized eggs so have both mothers and fathers. Let Bn bethe number of nth generation ancestors of a male honeybee. For example: B1 = 1 (itself), B2 = 1 (its mother), B3 = 2 (its grand-father and grand-mother), etc. Find a recurrence relation for Bn. [Assume that no honeybee appears more than once in the ancestral tree; that is, each honeybee has at most one child in the tree.](b) Prove that if n is divisible by four then Bn is divisible by three.arrow_forwardSolve the recurrence relation, given: • ao = 3 • a₁ = 4 . • an = 5an-1-6an-2 Remember: • The theorem is an = c₁an-1 + c₂an-2. -b± √b² - 4ac 2a • The quadratic formula is O a O b Oc Od an = 5(4)" -2(3)" an = 5(2)"-2(3)" an = 5(2)"+2(3)" an = 5(3)" -2(3)"arrow_forwardFind the general solution of the recursive relation an an = a10 (3)" + α20 (-3)" an = (a10+ a11 n) (-3)" None of these. an = α10 (6)" + α20 (-9)" an = (α10+ α11 n) (3)" = 6an-19an-2, n ≥ 2.arrow_forward
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