2+1/n 1+1/n 2n + 1 2 2 for n → o. 1 In n+1

Q: calculate 1+3+5+...+(2n-1) for n = 1,2...,6.

A:

Q: 2n+2 52n+1 3n+2, 22n+1 is divisible by 19 co dady M N [ day f04+ 204d (21)

A:

Q: n If E (ak + bk) 2n and n+1 k=1 E(ak – br) +, then ak = n n+2 k=1 k=1 3 2 5 2 O None 2

A:

Q: Let P(n) be the statement that n(n + 1)(2n + 1) 12 +22 + .. +n? for n>0 6. What is P(1)? a. It…

A: The given statement is

Q: "Co 34 "C, "C, "C; (-1)" "C, ,ne Nis equal to 10 14 (4n + 2) 2" n! 2"-n! () 3.5-7...(2n - 1)(2n +1)…

A: We have use binomial theorem  1-xn=nC0 - nC1 x + nC2 x2  + .........+(-1)n   nCn

Q: ) 6. Express the sum 9 + 28 + 65 + ... + (n'+1) using E-notation.

A: We have to find sum of series:

Q: 00 8tan-in Zn=1 n3D1 1+n2

A:

Q: For every positive integer n     12+22+32+...+n2=n(n+1)(2n+1)/6 Let S(n)=12+22+32+...+n2 How do…

A: See the attachment

Q: 1.-Proof by mathematical induction that 5 + 9 + 13 + ··· + (4n + 1) = n(2n + 3) ...

A:

Q: 3 Which of the following expressions are equivalent to 6n2 +12n 18 (n+2) C 6n (n+2) 18n + 38 A 6n…

A: The addition(subtraction) between two like fractions can be done by adding(subtracting) the…

Q: prone 2 + 4 + 6 + + 2n = n(n+1). for every nz 2.

A:

Q: Prove by induction that 3" <n! for all integers n with n ≥ 7.

A: As per the answering guidelines we will solve the first question only. Please upload the other…

Q: Using mathematical induction, prove that this equation holds for any n 2 1: n(n + 1)(n + 2) 1x 2+ 2…

A: Follow the process below and use induction first replace n with k and then n with k+1.

Q: hich of the following expressions are equivalent to 2n 4n2 + 4n n+ 5 4n2 + 6n 10 (n+ 1) C 4n (n+1)…

A: given,

Q: 5. Find and prove a formula for P(n,n-2) for n2 3.

A:

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

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

A:

Q: Prove that 3|(52n – 1) for all ne N.

A: We prove it by mathematical induction. 1st step We show that the statement is true for n = 1.…

Q: Show that. 1 (n + 1)(n + 2) n=1

A:

Q: 5. • Use induction to show that for n ≥ 1 we have (3n+ 1) + (3n+4) + (3n+7)++ (6n-2) M n(9n-1) 2

A:

Q: п(п + 1)(2n + 1) 2. Prove that 12 + 22 + 32 + 4?+ ...+n2 for every positive integer n. 6.

A: Here we have to prove that       12+22+32+...+n2 = n(n+1)(2n+1)/6    for every positive integer n .

Q: nCn-3= A. n(n+1)(n-1)/3! B.n(n-1)(n-2)/3! C.n(n+1)(n+2)/3! D. None of these

A: Solution: We have to find: