6. Find a such that 1 1 ¹ + ² + ( 1 ) + ²√ ( ? ) + · .. 2 3 . + n 1 n+ 1 (2) = a n+ 1

Q: (5) 7(3k – 1)² +26(3k – 1)–8

A: On simplifying the above expression,we get

Q: Show that P(n, 1) + P(n, 2) = (22) – 2 (2), for integers n ≥ 2.

A:

Q: 6x + 5 > -2(x – 3) – 25

A: 6x + 5 > -2(x-3) - 25 6x + 5 > -2x + 6 - 25 Add (2x) on both side 8x + 5 > -19

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

A:

Q: Find a formula for ¹ - 1²/ (²1) + 1² ( 2 ) -—- ... ₁ (2). (G) + (-) + I u

A:

Q: 21 divides 4(n+1) + 5(2n-1) whenever n is a positive integer.

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Expand and simplify    (i) (2k − 3)(k − 2)

A:

Q: a. 3.2F> Fn+1 for n23 [Solutions and final ans

A: We need to prove 2Fn>Fn+1 Now, we have formula for fibonacci sequence is Fn=Fn-1+Fn-2

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

A:

Q: In(+2)-3

A:

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

A:

Q: Jana!

A:

Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

Q: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

A:

Q: S(10) for √3 - 3 + 3√3+...

A:

Q: Find a formula for +(−1)n. (2). 1 1 ¹ – ²2 ( ² ) + ² ( 2 ) - -· ··- 1 n+1

A: To Find: A formula for .

Q: Consider the function f (same as in the previous problem) defined on the interval [0, 10] as…

A: Given Data: fx=35xx∈0,53x∈5, 10-y''=λy, y0=0, y'10=0To find: cn

Q: r4 3. |2ª – 8| d.x Jo

A: Use the property of modulus, 2x-8<0   when  x <32x-8>0   when x >3 So, 2x-8=-(2x-8)…

Q: (а) 3x< 5х—8

A:

Q: Which of the following is true? Select one: a. (n+1)= n(n) for any real number b. г(n) = n(n+1) for…

A: The objective of the question is to determine which of the given mathematical statements is true.

Q: (:)? /3 9. Which of the following is equal to (b) (–1)"-12·5., 3"n! 3.5-7..... (2n + 1) (Зп — 4)…

A:

Q: 4. Find the first three terms of (3x – 2)20. What is the coefficient of æ10?

A:

Q: For each positive integer n, define an = ((2+√3)" + (2-√3)") 2 It is known that an is a positive…

A:

Q: 1a.) 0x**3  + 9x**3  1b.) 4X**3  - 9x**5  1c.) (3x   + 1x**3) + 2(9x**3 +(-3x)) 1d.)…

A: 1a.) 0x**3  + 9x**3 1b.) 4X**3  - 9x**5 1c.) (3x   + 1x**3) + 2(9x**3 +(-3x))1d.)…

Q: Find the nth term of (a, b, a, b ... ), (a) and .(b) are constants 1-(-1)" 1- (−1)n+1 -[-D" + 2 2 a…

A:

Q: For each integer n>1, let A(n) denote the sum of the integers from 1 to n. For example,…

A:

Q: Evaluate L-tcos 5t. 10s А. (s +25 )* s2 - 25 - (s² +25)* 25s C. - (s° +5)* s2 -5 D. (s* +5) 50s E.…

A:

Q: min z= 2x, + 3x2 s.t. 2 + x24 X - X 2-1 X1, X 20

A: (Solving the first question as per our guidelines. Please submit the remaining questions separately)…

Q: п(Зп + 1) 2 + 5 + 8 + ... + (3n – 1) =

A: We have to prove the series  2+5+8+...+(3n-1)=n(3n+1)2

Q: 28+7 Find L-¹{²4)(+2)}. −4)(8+

A: