Given that 1+ 2+3+..+n = n(n+1) 2 , then the sum 50 + 51 + 52+...+ 70 =

Q: If the sum exists, enter the exact answer. If it does not exist, enter NA. 6+6⋅2+6⋅22+⋯+6⋅212=

A:

Q: 43 Compute for the sum. Answer directly. 2 3 ΣΣ11;3 i=0j=0

A:

Q: 1. Find a formula for the sum: 2+ 6+ 10 ... + 2(2n - 1)

A: The given sequence is 2+6+10+... +2(2n–1).

Q: For every natural number n,1+3+5+7+···+ (2n-1)= n^2

A: We prove the given statment by the principle of mathematical induction as in next step.

Q: If Sn denotes the sum of the first n terms of an AP prove that S30 = 3 (S20-S10)

A:

Q: A sequence is said to be decreasing sequence if Vn >1 2n.a O n+1 'n²³n+1·bO n+ n+1dO n+ 1

A: Given a statement

Q: Given the sequence Of (n)=2+2 Of (m) = 2 + 1/ n Of(n)=n+: 1+n Of (n)=3--1/ = 21/1, 23, 2441... what…

A: The given sequence is 212, 213, 214,... The objective is to find f(n). A map from ℕ to ℝ defines a…

Q: Write the first four elements of the sequence. n+1 3n -1 O -1, 1, O 0, 1 1 3 2'4 O1.1 3 2 3'2' 4'3 O…

A: The given sequence is n+13n-1. The objective is to obtain the first four elements of the given…

Q: Find of the following the Sum scrics. 2. 1- In(10)+ 2! る!

A: The given series is, y=1-ln10+ln1022!-ln1033!

Q: For all integers n, if n2 is odd then n is odd.

A:

Q: a) If d is an integer such that d | n + 5 and d | n² + 1, then d | 26. b) If n is a multiple of 26,…

A: a. Given that d is an integer such that d|n+5 and d|n2+1.

Q: The small positive integer n for which (1+i)?"=(1-i)?n is =..

A:

Q: Find the sum of 73 ㅈ5 11.3 3.5 ㅗ ㅈ - + ㅈㄱ 15.7 + n-1_2n+1 ㅈ (1)h 12n-1 (2n+1)

A: We can solve as follows

Q: Σ (-1) n=1 nyerges for all n20

A: Please refer to the image below

Q: 3. Determine the sum 3. 42n+1 (a) 33n n=1 4.5n-1 ( b) Σ 32n+3 n=1

A: to find: Sum of the given series

Q: Can you assist  me in  verifing    that    for    all    n ≥ 1,    the    sum    of    the    first…

A: Here, we have to verify that ∀n≥1, the sum of the squares of the first 2n positive integers is given…

Q: Given that n(n+1) 1+2+3+ +n= 2 then the sum 30 +31+32 +. . +70 D

A:

Q: In each case, find the first 5 terms of the Sum and comgute S

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Q: For all integers n> 1, 2+4 + 6+ . ..+ 2n = n² +n.

A: Here we are going to solve only the first question and for the remaining question please post the…

Q: Express the sequence {an}∞n = 1 as an equivalentsequence of the form {bn}∞n = 3. {2n + 1}∞n = 1

A: 2n+1n=1∞ When n=1, a1=21+1=3 When n=2, a2=22+1=5 When n=3, a3=23+1=7 When n=4, a4=24+1=9 Therefore…

Q: If n is a positive integer, then (n + 2)! A = |(n + 1)! (n + 2)! (n+ 3)! is equal to (n+ 2)! (n +…

A: We need to find the determinant of the given matrix. To find the determinant we will use the…

Q: For how many positive integers 'n', n3-8n2 + 20n - 13 is a prime?

A: Introduction :

Q: 3(3 + 1) n = 3: Show that 1 + 2 + 3 =

A: To show that 1 + 2 + 3 + ...  + n = n(n + 1)2 is true for the given value of n.   Also, to show…

Q: (-1)*-1 '(nIn n)? n=1

A:

Q: Which of the following does not represent the sum 9+11+13+15+17?

A: We have to find which do not represents the sum  9 + 11 + 13 + 15 + 17  Now ,  Check all 4 options…

Q: Consider a sequence generated by the formula ​f(n)=3n-9​ starting with ? = ?.

A: Consider a sequence generated by the formula ​f(n)=3n-9​ starting with

Q: For every integer n > 1, 2+4+6+ + 2n = n² + n.

A:

Q: Find the first four terms in the sequence. 2" 3) а a 2n + 1

A: solution.

Q: (봄) + (주) - Evaluate the sum 2.3 (p-2)(p-1) +. ...

A: As per the question we have to evaluate the given partial sum involving Legendre Symbols.

Q: what is the sum from k=1 to k=infinity of 2k/(k+7k)?

A: To determine the sum.

Q: Use the rules for sums of powers of integers to compute the sum. 24 4.² k=8

A: Recall: sum of squares of n integer                    ∑i=1ni2=n(n+1)(2n+1)6

Q: There were n topics (n >= 2) on an exam, from which a student drew two. Calculate n, knowing that…

A: It is given that  There were n topics on an exam, from which a student drew two. So, the number of…

Q: Use Gauss' trick to determine the sum 1+3 + 5 +... + (2n – 3) + (2n – 1) + (2n + 1

A: Gauss's trick is very significant in determining the sum of a series. This method includes the…

Q: n(n+1) for all n EN, • Given that 1+ 2 +3+..+n = the sum 70 + 71+72 + .+ 100 = 2

A:

Q: #2. Find the sum of the 8 n=1 1 (3n+ 1)(3n+4)

A: In given series we break the nth term of series as addition of nth term of two different series…

Q: prove the statement is true by using Mathematical Induction.

A:

Q: 7. Which of the following does not represent the sum 9+11+13+15+17? (1) E(2n+5) (θ) Σ(2-1) n=2 n=5…

A:

Q: Suppose that an = 5 and b, =1 and a =7 and b, = -9, find the sum of the series: n=1 n=1 A. (-5a, +…

A:

Q: (b). For all positive integers n 2 2. (") = 2 (5) + n².

A:

Q: 6. Find the value of each of the sums. a) E= om= b) E-,2³ = c) E-,(3' – 2)= d) Ek = 78

A:

Q: 14. Find the Sum of: 1 in(n+3) In (n+2) ニ

A: To find the sum of the given term

Q: What are the terms ao, aj, a2, and az of the sequence {an}, where an equals b) (n + 1)"+l? d) [n/2]…

A: a. an=2n+1. The terms become a0=20+1=1; a1=21+1=3; a2=22+1=5; a3=23+1=9 Therefore, the terms of the…

Q: Compute for the sum. Answer directly. Lore ΣΣ (-)) i=1j=1

A:

Q: 12(5" (8") n=1

A:

Q: Consider the sequence 1 4 4' 5' 6' 7 1 2 1 2n-2 1 0, ... a2n-1 a2n 3 2n-1' 2n Which of the following…

A:

Q: a) Show that from number 1, 2,... , 100 it is possible to select 50 different numbers such that the…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Find the sum of 73 75 + [ 2ㅈ 11.3 13.5 ㅈㄱ 15.7 + + (-1) 7- 2n+1 12n-1 (2n+1)

A: The objective is to find the sum of 12ππ31!.3-π53!.5+π75!.7+......+(-1)n-1π2n+1(2n-1)!(2n+1)

Q: If P(n): 2n < n! , nEN then P(n) is true for all n 2... None n23 n22 n24

A: If P(n):2n&lt;n!, n∈N then P(n) is true for all n≥...

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.