Problem2 Let n and k be integers with 1 ≤k≤n. Show that 2+2 ( 7 ) ( k ² ₁) = (²²+²7). 2 Σκ=1 - (²72)

Q: . What is the coefficient of a" in (2 – x)"?

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Q: |x+7/2| ≥ 9

A: Given,

Q: 2+² = (16*-¹)(2)

A: The given equation .We have to find the value of that satisfies the equation.

Q: 3 21. (k +1) k=1

A: The given expression is, ∑k=13(k2+1) To find the sum of the expression from k=1 to k=3 substitute…

Q: 133. -Σ 2" Sn+ -(x + 2)" n=0

A: Consider the series, Rewrite this as Now take the constant outside,

Q: 5x 3) x+4 хр-

A: Explanation of the answer is as follows

Q: UIN (x − 1) − = (x + 2) = 7

A:

Q: 21 (s+ √2) L-¹ {-

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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: Find 1 (9) Lp(p – 1). p(p²-1)3 (10) L-1 (p2+1)2,

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Q: 9. -2r - 7 >1 or x-2 2-1

A: we nee to solve the inequality -2x-7>1    or    x-2≥-1

Q: Please don't provide handwritten solution ..

A: The symbol Γ(n) represents the gamma function, which is an extension of the factorial function to…

Q: True or false: If a,b,m are integers with m > 0 satisfying m|(a^2 − b^2), then m |(a −b). Justify…

A: Given Information: If a,b, and m are integers satisfying m|a2-b2. To check: m |(a −b) for any…

Q: 3 3) 4 x-= 5x - 22

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Q: 2. The sum of three consecutive positive odd integers is always a multiple of (A) 3 (B)5 (C)7 (D)9…

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Q: **For what c value is (x-5) a factor of x³ + 2x2 + cx + 10

A: According to our company guidelines we are supposed to answer only one question since you have asked…

Q: 9. Solve In (x+5) 2 2. O A. (x | x 2 12.3891} B. (x | x 2 2.3891} O C. (x |xs 12.3891} O D. {x |x s…

A: Given:         ln(x+5)≥2

Q: 3x²³-2x² + 3kx + 18 by x- 6 to be equal to zero, k must be equal to.

A: Use division

Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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Q: 20. S dr √3-4r-r²

A: On solving this we will get

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

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: 7. For n ≥ 1, verify that 12+32 +52 ++ (2n- +3²+5² · + 2n-1)² = (2n+1) 3

A: Ans : page 1:Ans page 2:

Q: 21 84 = 1, where x and y are positive real numbers, find the smallest possible y of x + y. If + X…

A: Given   21x+84y=1

Q: 1- x**! 1- x n+1 6 (x # 1) r=0

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Q: If p = 4x³ + x² + 2x + 5 and          q = 6x³ + 3x² + x + 2  Find ||p||  and ||q||

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Q: For the following claim Below you must disprove it. "For all integers x, x^2 + 1 is odd" Use the…

A: for example take x=3 .  then x^2 +1=10 , which is even.

Q: п(п + 1) Show that , k 2 k=1

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Q: e3x + 6 enx e(n+1)x = 1+ e® + 2 Sx n! (n+ 1)!

A: The given series is : eex=1+ex+e2x2+e3x6+·····+enxn!+en+1xn+1!   Let fx=ex The above function can be…

Q: Show that (n + 1)! > 2"+3, for n > 5.

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Q: n(n-1) 2 this statement to justify the following. (n+³) = - :)-( (equation 1). 2 (n + 3)(n + 2) 2…

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Q: S(in 6x) dx x (In 6x)2 - 2x (In 6x) +c x (In 6x)2 - x (In 6x) + x + C <(In 6x)2 - 2x х (in 6x)2 + 2x…

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