The general combinatorial formula for the nth triangular number (1, 3, 6, 10, 15, 21, .) is On+1Cn OntiC2 O 2n Cn On+iCn-2

Q: 16 M = 7 -5 Find formulas for the entries of M", where n is a positive integer. M" =

A: We have to find the entries of matrix Mn.

Q: Find the index of 12Z in 3Z

A: The integers are

Q: Simply the expression to a sum of 2 terms and then factor the result to obtain the product of sums:…

A: The complete solution is in given below

Q: Which statement is not correct? 4 · 10^(2n) + 9 · 10^(2n−1) + 5 1 is divisible by 5 2.is divisible…

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Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m ) + ( - n ) = - ( m + n)

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Q: How do I prove that 4 divides 32n-1+1 with induction? (n is natural numbers)

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Q: This will be (n+k-1)= 29+6-1 29 -¹1) = 34 29 = 278, 256.

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Q: If n is a positive integer prove that 3^(2n) - 26n -1 is divisible by 676

A: if n is a postive integer prove that 3^(2n) - 26n -1 is divisible  by 676

Q: A) (1 + √₂)² B) (1 -√2)² c)(1+√2)(1+√-2) D)(1+√2)(1-√√2) E)√2² + (√2)² Which of the above…

A: A) 1+22B) 1-22C) 1+21+2D) 1+21-2E) 22+22

Q: bers {1, 3, 6, …}

A:

Q: . Evaluate 3 √√9-x² √9-x²-y² IL! z√x² + y² + z²dzdydx -3-√√9-x² 0

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Q: For 7-10 Given a_1= 3, a_2= 7 and a_n= [2a] _(n-1) + a_(n-2) for n 23, 7) Find a_3 =,* Your answer…

A: First Question: (7) Given a1 = 3 , a2 = 7 and  an = 2an-1+an-2 then a3 = 2a2+a1 = 2*7+3 = 17 Hence…

Q: 9. Use fix) = 3-4 and gix)-5-2' to evaluate the expressions in simplitied form: * (g )

A: We have the given functions as f(x)=3x-4g(x)=5-2x3   We have to find (a) f∘g(x) (b) g∘f(x)

Q: Let n be a positive integer. Using congruences, show that 3n+3 +23n+3 is divisible by 7.

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Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

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Q: Show that this number is Irrational number

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Q: Sorry but the answer I got given was wrong! Is there any other answer to the nth term of 15,12,9,6…

A: Given:    Arithmetic sequence : 15 , 12 , 9 , 6

Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3…

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Q: Which of the following gives the Binet form of the nth Fibonacci number? O Fn = Fn = Fn = Fn =…

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Q: ne order of the element 16+ in Z24/ is None of the choices 8.

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Q: If a and b are distinct integers prove that a-b is a factor of an -b" whenever n is positive integer

A: if a and b are distinct integers prove that a-b is a factor of a^n - b^n whenever n is positive…

Q: 5. Prove that n² is an even number if and only if 3n + 1 is an odd number by proving a) If n² is…

A: To Prove: We have to prove that n2 is an even number if and only if 3n+1 is an odd number.

Q: Find a formula for the general term a, {5, 8, 11, 14, 17, .} 5n + 3 On+3 O 3n + 2 O 2n + 3

A: We can answer the question as below

Q: Show by induction that 4 divides 2m^2 +6m for an integer m>0

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Q: 5 =5 Hence, 6"-1 is divisible by 5 is (10.). for n=1 Part 2: Assume that 6" - 1 is divisible by 5…

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Q: Please provide justified answer asap:::: Show that n is odd if and only if n^2+4n+1 is even.

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Q: Find the 66th term of the triangular numbers {1, 3, 6, …}.

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