k+4 n(3n +7) k(k +1)(k + 2) 2(n+1)(n+2) k=1

Q: simplify  (3n+1)!/(3n-1)!

A: Given:

Q: 2k + 1 k(k +1) k=1

A:

Q: (n+14)2

A: Given expression is,

Q: (2n)! – (2n + 1)! (2n)!

A: It is required to find out , 2n! - 2n+1!2n!  For this we use factorial properties.

Q: So an = n 16 n+ 16 (n-1) 16 (n-1) + 16 = n - 16 n+ 16 I X 11 (n + 15) (n + 16)

A:

Q: (2+i)(1+3i) – 2+ 4i= 3i O 4+2i O 3+i O 3-i0

A:

Q: find (2n +1)! = 120

A: Here we have to find the value of n.  2n+1!=120

Q: Simplify the following expression: (6n4 – 2n2 + 4) – (7nª + 3 + 8n) + 8n - -n4 – 2n2 + 16n -n4 – 2n2…

A:

Q: 3) (n² + 10n+18) ÷ (n+ 5)

A: To divide the following expression.n2+10n+18÷n+5

Q: 2(2n+5)=9(7n+3)+8

A: Given equation 22n+5=97n+3+8 We have to find the value of n Use distributive property and then…

Q: n + 3n

A:

Q: (2p + 1)(p + 5) = 2p + 40

A: Solution: The objective is to solve the given equation

Q: V. (a) Find the product of: 1. (x+2)(x + 2) 2. (2x – 1)(2x - 1) (b) Make a general rule about…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Select all expressions that are equivalent to (2n +6)(n+ 3). O a 2(n? + 6n + 9) 2n+ 6n +18 Oc 2n…

A: Given,  => (2n + 6) (n + 3)  Taking '2' common from expression , => 2 (n +3) (n + 3)

Q: 00 (2n +1)" n2n n=1

A:

Q: 8+2z+6(z-1)

A: Given,

Q: How did they got n(n+1)(2n+1) / 6

A:

Q: (n + 4)3 =

A: Given query is to expand (n+4)3

Q: (k + 2)(12k3- 3k2 + k + 1)

A: The given expression is k+212k3-3k2+k+1.

Q: 2 + 8n = 6n + 3(2 + n)

A: Given: 2+8n=6n+3(2+n)

Q: k(8+3+k)=8k+3k+blank

A: We have to solve the problem

Q: 2(5)+5+1

A:

Q: 5 (4k + 3) k 1

A: Given,

Q: 35. Select each expression that is equivalent to 5(n + 4). O5n + 4 5n + 20 O 15 + 5n + 5 5(n + 3) +5…

A: We have to select expressions that are equivalent to 5(n + 4).

Q: 2(n-3)+n(2-n)=2-n2

A:

Q: a)(6n2– 3n + 9) - (n² + 3n – 5) b) (15a – 3w + 7) – 2(2a – 9) + (3w – 15a)

A: a) Given:         6n2-3n+9-n2+3n-5       =6n2-3n+9-n2-3n+5 combine like terms…

Q: 1 (2р + 9) p+5

A: Given equation, 12(2p+9)=-p+5

Q: 3. (4m2 + 2n) (4m2 - 2n)

A:

Q: 4) n +4n - 12

A: GIVENn2+4n-12

Q: Is 2n? + 12n + 18 equivalent to (2n + 6) (n + 3)? True False

A: Disclaimer-Since you have asked multiple questions, we will solve the first question for you.  If…

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.