Show that for any neZ, n is either n= 4k n= 4ktI or n=Yk+2 n=4 K+3 or

Q: value of ∑n=1∞(6an+9bn) if ∑n=1∞an=8 and ∑n=1∞bn=2.

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Q: if 3 does not divide n then 3 divides 2n^2+1

A: Let us Assumue 3 divides (2n2+1) n2+1=3λ Now  2n2+1=n2+1+1⇒(2n2+1)+(-λ)3=1⇒ gcd(2n2+1,3)=1…

Q: find the probabi lity of getting 3 on the 2nd olie given the Sum is 8?

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Q: Let M = {14*: kEZ*} and A = {7k:k € Z*}. Then

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Q: How many digits does a number 8^(n). 5^(3n+4)  have, if n belongs to N ?

A: Given data Number: 8n .5 (3n+4) We have to find digits in number.

Q: For positive integers m > n , show that -2 + n- 1 -3 + ...+ n + n-1 n - 1 + in

A: The right-side of the given equation can be expressed as…

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: . Show that n! > 3ª for n> 7.

A:

Q: 42. 8T n=1 (n!)" nin

A: Consider the series ∑n=1∞(n!)nn4n   To Find: whether given sum exists or not i.e., given series…

Q: | . ८ g in 6022 on T 3x Symbolic hotation and fractions where needed) Use

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Q: Show that if 5 divides n2 with remainder 4, 5 divides 3n3 with remainder 2.

A: Given that 5 divides n2 5 n25 n×n5 n5 n3 As it gives the remainder 4 on dividing by 5. Therefore it…

Q: Show by mathematical l Induction y 4n-2 3. +17 can be divided by +22 possitive integers 16 far all

A: To prove the given statement by using mathematical induction.

Q: llowing is true for the ser 8 Σ n=1 n 2n + 1 = others to 2 to 1/2

A:

Q: 1. Find a counterexample to show that each statement is false: The sum of three multiples of 5 will…

A: Counterexample is to show the statement false by proving some example is wrong with the statement.…

Q: (-1)" n In n n=2 5.

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Q: Find a simple closed expression for computing E=1k²Hx and verify your answer for n = 4.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Obtain the sum of the seri Ean $a = -² 2 n=2 nn

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Q: How did they got n(n+1)(2n+1) / 6

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Q: 2) (n² – n – 29) ÷ (n – 6) 4) (k² – 7k + 10) ÷ (k – 1) tv

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Q: Isit true that n? + 1 € N(n)?

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Q: * if the o is not known and (n< 30) can be used z O

A: Which one is the correct choice

Q: As sume that L1 is not paralelo to L2 explica why ángulo 3 not paralelo to ángulo 7

A: We have to explain why angle 3 and angle 7 not parallel.

Q: If in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n ,then prove that…

A:

Q: ind p hat if x is 7 and n is 10

A: The provided information are: Number of success (x) = 7 Number of trials (n) = 10

Q: Q)1 a) How many 3 digits passcodes are there if first digit must be a 1 or 2 ?   b) How many 3…

A: Q1) a) There are 10 digits 0,1,2,3,4,5,6,7,8,9. The 3 digit passcodes must be formed such that first…

Q: Droof that n! %3D1 オ=O K!(n=k)!

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Q: If A =P-BP then B=Q-lAQ for o-1=P- True False

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Q: 8 of 22 If č = (-3, –5) and d = (-2, –6), find |47 – 2.5d|. V74 O 8/6 O 7/5 146

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Q: IS SIX ba ch has an upcoming game against State on I State employs five different defenses. Th rards…

A: Q

Q: Solve for n in permutation 9(n²-1Ps) + 9(7²P6) = n²+1 P7 %3D

A: Let's find.

Q: (-1)" In(nº) Σ 20. 4n n=2

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Q: Give a direct proof of the claim: V n E N, Vk E N, if the last k digits ofn are divisible by 2k then…

A:

Q: v. n! = 0(n")

A: We will answer the question 5 only as we don't answer multiple questions at a time. Please resubmit…

Q: If an = n+ 3", n > 0 then choose the correct option a3 = 2a2 – ao +7 az = 2a2 + ao –7 az = 2a2 + a1…

A: Recurrence relation

Q: Show that n! > 3ª for n > 7.

A: The given inequality is, n!&gt;3n We need to prove that, the inequality is true for n≥7 Firstly,…

Q: Show that n! > 3 for n ≥ 7

A: We have to prove this assertion that, n! &gt; 3  for n≥7 We will prove this statement by the method…

Q: O Given 20 balls of different colors and 10 bananas, find the number of ways to distribute i-The 20…

A: As per Bartleby guidelines, we are advised to answer one question at a time, I have given you the…

Q: 4. Use a combinatorial argument to show that () n 1 -2) n + 22 n 2 3 -

A: Given: nn-2=n3+12n2n-2n

Q: nEZ is odd if 3kEZ: n=2k. O True O False

A: Since you have asked multiple question we will solve the first question for you. If you want any…

Q: if m is odd and n is odd, demonstrate that m*n=odd

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Q: (c) Show that for 2" > 4n for n ≥ 5.

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Q: Solve for n: 6(п — 4) 3 а(n + 3) - Preview = U

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Q: If P(n) is the statement "n' + n is divisible by 3' Prove that P(3) is true but P(4) is not true.

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Q: Show that 2^n &gt;=1/8 for n&gt;= -3.

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Q: 1 - evaluate 2 n =0 n +7n+

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Q: If n is 0 what is 8n

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Q: Find n, if 3n+18=0

A: Linear equation question

Q: Find n in P(n,n-1)=6

A: Given that P(n,n-1)=6 find n

Q: Abby notices that for the first twenty perfect squares, each square is either a multiple of 5, one…

A: If n is a natural number, then n2 can be written as 5k- 1,5k, or 5k +1, where k is a whole number.…

Q: ove that n’ +5n is divisible by 6 for all n E N.

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.