Prove that there is no hooked Skolem sequence of order n= 8.

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim Sn = .…

A: Limit of a sn

Q: Let Fn be Fibonacci sequence. Prove that:

A: By the definition of the Fibonacci sequence, Fn+2=Fn+1+Fn and the Fibonacci sequence is satisfied…

Q: **) Define a sequence a1, a2, a3, ... as follows: a1 = 1, a2 = 3, and a, = an-1+ an-2 for al ategers…

A: The given sequence is 1,3,4,7,11,18,..... such that an=an-1+an-2 We have to prove P(n): an≤(74)n for…

Q: If (an) is a sequence converging to L, with an 20 for all n, prove that L≥ 0 and that (√an)1…

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Q: Consider the sequence {ax}, defined by а, 3D 1, ад — 1, and ak 3 а-1+ ak-2 for k > 3. Compute as.

A: We have given two terms of sequence {a_k}, a_1=1 and a_2=1 and then sequence {a_k} is defined by…

Q: Let {n} be a Cauchy sequence. Prove that {s} is bounded.

A: Given: In this question, the given details are, Let {sn} be a Cauchy sequence. To Prove that {sn} is…

Q: Exercise 5. Let l be any positive integer. Use sandwich theorem for sequences to prove that the…

A: Sandwich theorem :- Let un,vn,wn be three sequence of real numbers and there a natural number m such…

Q: Show that the sequence {1, -1, 1, -1, 1, -1, ..., (-1)n+1, ...} diverges.

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Q: Let {Sn} n=1 to infinity, be an unbounded sequence of negative numbers. Show {Sn} n=1 to infinity,…

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Q: Let (n) be an unbounded and increasing sequence of real numbers. Prove that (xn) diverges to +∞.

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Q: Prove if ( a n ) is a Cauchy Sequence and ( a n ) has a subsequence that converges to L, prove that…

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.