Use ibn al-Haytham's procedure to derive the formula for the sum of the fifth powers of the integers:    1^5+2^5+...n^5=1/6 n^6+1/2 n^5 +5/12 n^4 - 1/12 n^2

Q: One term in the expansion al * (x + a) ^ 7 = 756x ^ 5 Numeric Response The value of a, if a>0 is

A:

Q: Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible…

A: The given statement is " The possibility to raise a positive number b to a power and obtain a…

Q: In a sequence of 12 numbers, each term, except for the first one, is 12^11 less than the previous…

A:

Q: (a) On a certain computer system, a valid password is a sequence of 6 to 8 symbols. The first symbol…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: (n^2-n)+((n-1)^2-(n-1))+....+(1^2-1) =n(n+1)(2n+1)/6 - n(n+1)/2

A: We shall first derive the formulas for sum of first n natural numbers and sum of squares of first n…

Q: this sequence 31 27 23 19 Explain in detail how you could find the 10th term

A:

Q: ) Find an integer having the remainders 3, 11, 15 when divided by 10, 13, 17, respec- tively.…

A:

Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

A:

Q: 24. Give a recursive definition of a) the set of odd positive integers. b) the set of positive…

A:

Q: find the nth term

A: Step 1: Step 2: Step 3: Step 4:

Q: bers {1, 3, 6, …}

A:

Q: Use the binomial theorem to show that 72 Σ(1) ( **(?). i-0 0.

A: Use binomial theorem to show that given formula.

Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3…

A:

Q: hat is the last digit in the product of (3¹)(3²)(3³)(34)...(34⁰⁰)?

A:

Q: Write the first 3 terms of the expansion of (3x - ) – 2)" and simplify |

A:

Q: What is the 100th term of a sequence of number in which, for every positive integer x, the sum of…

A: In the given question, concept of summation series is used. Summation Series The total of the series…