Use Mathematical induction to show that H sub(2^n) is less than or equal to 1 + n.

Q: /Find the sixth term in the expansion (x- 2y)"

A:

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: plz solve q4

A:

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: Does it converge: ∑(sqrt(n+1) - sqrt(n))/sqrt(n2+n) if so what is the sum (show steps please)

A:

Q: There are 8 people in a room, whose ages are between 10 and 40. Show that we can always find two…

A: Pigeonhole principle Here, we don't know the ages of 8 people, but we know the range of sum of their…

Q: Briefly explain the differences between ‘mathematical induction’ and ‘strong induction’.

A: Remark:  Mathematical Induction: Let P(n) be a statement defined for all integer n. Then suppose the…

Q: State binomial Theorem.

A: Statement of Binomial theorem.

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: Prove by mathematical induction

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: How many positive integers less than 850 are multiples of 8, 3, or 5? Use the Principle of…

A: Using the Principle of inclusion/Exclusion, the formula for A∪B∪C can be written as:…

Q: V nEN, 7"- 3n is a multiple of 4.

A: We have to find   For all n= natural number we have to

Q: Find the Sum to infinity of the sea tès - Ce30 t ces 20 - 1-3 1-3.5 ces 30 + - (-nCBCIT). 2.4 2.4-6

A:

Q: Use sigma notation to write the sum.

A:

Q: Express the repeating decimal, 0.529529529... as a fraction in lowest terms.

A: It is required to express the repeating decimal as a fraction in lowest form.The given repeating…

Q: Prove: The sum of an odd number of odd numbers must be odd.

A: Let us prove this by induction, that if n is odd and a1,a2,. . .. .an are odd, then ∑i=1nai is odd.…

Q: Find the term indicated in the expansion .

A:

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

A:

Q: Express the sum in terms of summation notation. (Answers are not unique.)

A: Given: 12 +25 +38 +411 To express: The given sum in terms of summation notation.

Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

Q: How prove That ()

A: Just try substituting z=x+iy and simplifying.

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

A:

Q: What is the 5th term in the expansion of

A: The 5th term of the given expansion is solved by using binomial expansion formula (X+Y)^n.

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

A:

Q: Find the sixth term in the expansion (x-2y)"

A:

Q: Find Exponential Family 4-{N(0,1),0 € (-∞,+∞) }

A: Dear student, If you find this solution helpful please upvote ? it.   Here in this question it has…

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: Sx" Inxdx

A: The given integral is  I=∫xn ln x dx after solving this we have to use the result to find the below…

Q: Use the binomial theorem to expand (1-x)^5

A:

Q: Does a geometric sum always have a finite value?

A: Given :                  The geometric sum always have a finite value ?

Q: Please help n show steps

A:

Q: Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

A:

Q: Use mathematical induction to prove: For each natural number n, 6 divides (n3-n). I need to write a…

A:

Q: Find the sum of the first 20 positive even integers.

A:

Q: DEFINE Binomial approximation

A: Binomial approximation: The normal distribution can be used as an approximation to the binomial…

Q: Find the sum of first 24 terms of the list of numbers whose nth term is a. 3+2n

A:

Q: Find the coefficient of the term involving x* in the expansion of 3x – - -262444 c. -252440 а. b.…

A:

Q: What is the last digit when you expand 3^2005 ?

A: Topic - exponents

Q: Use binomial theorum to expand (1 + 1/x)^7

A:

Q: Find odd and general

A: Given,       f(x)=x-π3;   0≤x≤π

Q: ition to prove the n positive number. of Your Your answe that 1/x 00 as

A:

Q: express using sum notation

A: The series represents  sum of cubes

Q: Fermat's theorem is true for only prime number. إختر واحداً.

A:

Q: Find the sum of the first 80 positive even intergers.

A: Sum of the arithmetic progression with for n terms where a1 is the first term and an is the last…

Q: d the image of the point (-2,4) under the expansion with factor 2 in the direction. ) (2,8) (-2,8)…

A: Given query is to find image of the point after expansion.

Q: 5 divides n -n whenever

A:

Q: Find the sum of first 24 terms of the list of numbers whose nth term is a = 3 + 2n

A:

Q: Find the sum of all Integers between 84 and 719 which are multiple of 5

A:

Q: algorithm to determine the decimal number answer to 2893 ÷ 6 to the hundredths place. b. Interpret…

A: Solution of the problem as follows

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.