1. 1.1! +2.2! +3.3! + ... + n.n! = (n + 1)! - 1 for all n ≥ 1

Q: 1 + 1.2 1 1 n for all integers n>1 n+1 3. Prove that %3| 2.3 n(n+ 1)

A: To prove the given statement.

Q: n(n+1)(2n+1) Prove: 12 + 22 + 3² + ... +n? for all positive integers, n.

A:

Q: n3 + 3 n5 n4 - Prove that 14 + 24 + ..n* = +. n for all n > 1. 30 -

A: Consider the provided question,

Q: 4. Conclude that n2 n=1 ||

A:

Q: What is the summation from n = 1 to infinity, of  (3n+1) / (5n + 4) ?

A:

Q: Wht is the sum of this 8.1 - 3.1 x 2.1 + 0.4

A:

Q: Let n = WEE 5 Find n - 1. n – 1 =

A: Given:- n=-2/5 To find:- Value of n-1

Q: Indicate the smallest integer n such that (6x²+4x)³ f(x) = € 0(x¹). 2A-4x On=4 O n=2 O n=1 O n=6 O…

A: f(x) = (6x2 + 4x)3/(x4 - 4x)         = {2x(3x + 2)}3/{x(x3 - 4)}        = 8x3(3x + 2)3/{x(x3 - 4)}…

Q: Determine whether (5) () = (;) (") n-3 (where 3 < k < n) is true or %3D false. O True O False

A: We have given that

Q: X ME n! 3 11

A:

Q: n(n+1) For all n E N, prove 1 + 2 + ··· + n = 2

A:

Q: 3. Prove that 6|(9" - 3") for all n E Z+.

A:

Q: 3. If а, 1000". Find N E I, the set of positive integers, such that an+1 N). n!

A: Given an=1000nn!. We have to find the N∈I such that an+1&lt;an, n&gt;N. For n=1 a1=100011! For n=2…

Q: Prove that n Sk k=1 = n(n + 1)(2n + 1) 6 for all n € N.

A: To prove:We will use mathematical induction to prove this.Let