Determine how many terms of (-1)*+lgk must be summed to be sure that the remainder term k! k=1 is less than 10-5 in magnitude.

Q: If n be positive integer, show that the algebraic sum of the numerical coefficients in the expansion…

A: As given above that n be a positive integer. And the given expression is: 3x-2yn We have to prove…

Q: Expand (7 – 3x)“ in ascending powers of x, up to and including the 4" term. Hence, approximate…

A: We know (n+1)! = (n+1) n! Crn = n!(n-r)! r!

Q: Prove that the difference of squares of any two odd numbers is multiple of 8. (SOlve this task…

A: To proveDifference of squares of any two odd numbers is multiple of 8.

Q: Determine whether there are infinitely many primes that have a remainder of 12 when divided by 25.…

A: Given question is Determine whether there are infinitely many primes that have a remainder of 12…

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Consider the given expression. y3-12c29 The binomial formula is defined as,  a+bn=∑k=0nnkan-kbk As,…

Q: Find the least positive integer that yields the remainders 1, 3, and 5 when divided by 5, 7, and 9,…

A:

Q: How many terms are there in the expansion of (a+b)48 after like terms are collected?

A: This question is related to binomial expansion. We will solve it using given information.

Q: How many 3-digit positive integers exist that when divided by 7 leave a remainder of 57

A: 3 digit positive integers start from 100 and ends with 999. Least positive 3 digit integer which…

Q: Find the specified nth term in the expansion of the binomial. (x + 2z)7, n = 4

A:

Q: In a group, there were 115 people whose proofs of identity we passport, some had voter id and some…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder 1, 5 when…

A: Let x be the required number. The number is divisible by 3, so it leaves the remainder 0 when it is…

Q: Find the sum of n terms of an AP whose nth term is given by an=5-6n

A:

Q: When four positive integers are added three at a time the sums are 1551, 1659, 1720 and 1736. The…

A: when four positive integers are added three at a time the sums are 1551, 1659 ,1720 and 1736. we…

Q: A sequence of positive integers starts with one 1, followed by two 2s, three 3s, and so on. (Each…

A: Given:     The sequence is:     1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,... To get this number, we have to…

Q: If 6th term of a G.P. is 9375 and its 4th term is 375.Find its 9th term.

A:

Q: Prove the formula for the sum of the first positive integers:

A:

Q: Find the largest value of n such that: > (6k – 8) < 3000 k=1

A:

Q: Find the sum of the first 21 positive integers. The sum of the first 21 positive integers is

A: We will use the concepts of A.P.

Q: What are the coefficients of æ5000 and æ4999 in the simplified expansion of (5æª – 2)²2021?

A:

Q: Find the specified nth term in the expansion of the binomial. (x – 10z)7, n = 4

A: Known fact: The (r+1)th term in the binomial expansion of x+yn is given by Tr+1=nCr xn-r yr.

Q: does there exists   ______such that if n is divided by 5 the remainder is 2 and  if   ?

A: We have to check whether there exist n such that if n is divided by 5 then remainder is 2. Let if n…

Q: Show that if any eight positive integers are chosen, two of them will have the same remainder when…

A: Pigeonhole Principle- If n items are assigned to m containers, and m&lt;n,then at least one…

Q: If m times the nth term of an AP is equal to n times its nth term, show that the (m + n) th term of…

A:

Q: Find the 4th term from the end in the expansion (2a + 5b)8.

A: Let's find 4th term from the end.

Q: very third grade class has acert

A: The solution is given below

Q: Find the sum of the positive even integers up to and including 50.

A:

Q: Find: The sum of all positive integers less than 400 which are not divisible by 5.

A:

Q: The 11th termof an A.P. exceeds than 10h term by 7 find the commondifference.

A:

Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways

A: Let us have smallest prime numbers  are, 2,3,5,7,11,13 17,19.....

Q: (b) Find the sum of the first 110 positive odd integers.

A: Our Aim is to find the sum of the first 110 positive odd integers.

Q: 1. Find the sum of the first 50 even positive integers.

A:

Q: If in the expansion of (1 + n}+", the 5th term is 24 times the 3rd term, fnd the value of n.

A:

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: The Binomial Theorem is, (a+b)n=∑k=0nnkan-kbk Where, nk=n!k!(n-k)! The given question is to find the…

Q: Find the least natural number a with the property that the sum a + 2a + 3a + .. + 9a is the number…

A: Given sum is  a+2a+3a+4a+5a+6a+7a+8a+9a

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: The expansion of an general expression is given by (a+b)n=∑nkan-kbkk=0n  so any term can be found…

Q: Determine how many terms of (-1)*+12k k! must be summed to be sure that the remainder term k=1 is…

A:

Q: 6. Find the remainder when 721 divided by 43 7. For a given integer n, prove that 3 k-0

A: To find the remainder when 7221 divided by 43. Now, 7 and 43 are relatively prime and 43 is a prime…

Q: "For all integers n, n(n² – 1) is divisible by 6." (You may use quotient-remainder theorem and…

A: Let us consider, for all integers n a = n3 – n a = n (n2 – 1) a = n (n + 1)(n – 1)

Q: Can you think of the smallest number N such that ot can be expressed as a product of the two factors…

A: We have to find out the number N that can be expressed as a product of the two factors which are…

Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways.

A: The number is 22 and all others smallest integer can not be written as sum of two primes in three…

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given To evaluate

Q: Find the sum of all  natural numbers between 250 and 1000 which are exactly divisible

A:

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given expression: 3c+c247 Concept used for the general term:…

Q: If 6th term of a G.P is 9375 and its 4th term is 375.Find its 9th term

A:

Q: Find the 2nd term in the expansion of (a + b)6 in simplest form.

A: We can find the 2nd term as below

Q: Find the sum and product of each of these pairs of numbers (20CBA)16 , (A01)16- Express your answers…

A:

Q: Expand (3 – 7x)' in ascending powers of x, up to and including the 4th term. Hence, approximate…

A: Binomial theorem, (a-b)n=C0nan-C1nan-1b+C2nan-2b2-C3nan-3b3+...+Cn-1na1bn-1+Cnnbn To find binomial…

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.