et the terms a₁, a2, a3, ..., a, be in G.P. with common rat et S denote the sum of first k terms of this G.P.. Prove r+1

Q: 2 Find the sum of a 7+9+11+13+ to 10 terms b

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: . If n(A) = 15, n(B2)= 20, and n(A ∩ B) = 10,find n(A ∪ B)

A: Given: nA=15, nB=20, nA∩B=10

Q: Suppose that A, B, C, and D are digits from 1 to 9 and that A + B = CD (a) What digit must C be?…

A: Given that  A, B, C and D are digits from 1 to 9 such that  A + B = CD   (a)  If 1 ≤ A, B ≤ 4 then A…

Q: Q:Let S, denote the sum of the first n terms of an A.P. 3n = 6. S, = 3 S, Then prove that S.

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Q: determine the value of c(n,5) /p(n,5) where n can be any integer thats 5 or greater

A: Recall the following. Permutations Number of permutations of n things taken r at a time: pn,r=n!n-r!…

Q: (26) Are there natural numbers n, m such that 20" = 50m? Justify your answer with a proof or a…

A: The idea is to use a prime factorization of the numbers 20 and 50 and then use this to solve the…

Q: Q. 02: (a) Verify the commutative propernties of union and Intersection with help of A = (1,2,3,4),…

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Q: Prove by induction that it is possible to pay, without requiring change, any whole number of…

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Q: The factorial of n is the product of all positive integers less than or equal to n. It is…

A: Note:Hey there! Thank you for the question! We have solved this problem using trial-and-error…

Q: 0-2 1 -2 0 0 0 duced echelon form of the augmented matrix [A b] i 1 (a) Express the general solution…

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Q: 3. Let n be an integer, show that if n is even, then n is also even using indirect proof.

A: Given : Let n be an integer.   To show that if n2 is even, then n is also even.

Q: 3. Let x be an integer. Use the previous result to prove the following corollaries. (a) If x divides…

A: Divisibility: If a and b are integers, we say that a divides b, and write a|b, if there is an…

Q: f(x) = x^ Is f'(x)=nx-1 Where nER.

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Q: nd the smallest positive integer N such that n+2 3n-4 -}| < < 0.01 for all n ≥ N.

A: We want to find N such that n+23n-1 - 13 &lt; 0.01    for all   n ≥ N

Q: A box contains six discs numbered 1 to 6. Find for each integer k from 3 to 11, the probability that…

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Q: Let p, q, and r be prime natural numbers with p # q and n= p2q. Then, all the subfields of GF(r")…

A: Answer: Option (C) Given that, p,qand r are prime natural numbers and n is positive integer. Let F…

Q: Proposition 14. The Fibonacci numbers are defined to be F1 = F2 = 1 and F, = Fn-1+ Fn-2 for n > 3.…

A: Given The Fibonacci number are defined as F1=F2=1  &amp; Fn =Fn-1+Fn-2 , n≥3 then we have to show…

Q: Prove that 2n + 3n is a multiple of 5 for all odd n € N.

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Q: 5) Let n be a positive integer such that 7 | (8-1). Prove that 7 | (8=*1 - 1). (Hint: Rewrite 8*1…

A: Given: Let n be a positive integer such that 78n-1. To prove: 78n+1-1

Q: Prove that n>= 12 is a sum of two composite number.|

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Q: Format: [*10^] . Indicate the sign only when it is negative. • Consider only 5 decimals for the…

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Q: The sum of the terms 1 for k= 3, 4, ... 10. Provide your answer below: || ])

A: The series given is  3+4+5+6+7+8+9+10 Now asked to find summation notation of the given series…

Q: Prove that if n is a natural numbers grater than 1, then ni +1 is odd.

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Q: Which of the answers below is the ordering of these running times from fastest to slowest? a)…

A: We have to arrange the following sequences in order from fastest running times to slowest. (a)…

Q: If p, q, r are prime numbers such that pqr = 19(p + q + r) then the value of 2(p + q + r) is

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Q: 12. Prove that if gcd(a, n) b, then ax = b (mod n) has no solutions.

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Q: 3 = 2/3

A: We have to simplify the given expression  (34-25)÷23

Q: : Use he comparism test to prove hat n-2 Converyes

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Q: Prove that tim 51

A: Thanks for the question :)And your upvote will be really appreciable ;)