3 1 b- k +1 k=0

Q: k+4 k-1 k+4 1. 4 4 4k

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: >k = 1 + 2 + 3 + · · · + n = ... k= n (п + 1) (b) (а) п! 2 п (п + 1) (2n + 1) (d) (с) nk

A:

Q: P (-3 < z ≤ 0)

A:

Q: (1 + x) – Σ - (n).", -Σ n=0

A:

Q: 2 + 3 R + 8 k=1 8

A:

Q: 2(3 – k?) а. k=1 6 b. E – 5) (k² - 5) k=1 5 Σ > k(3k + 5) С. k=1

A: I am attaching image so that you understand each and every step.

Q: K+1 – /K k=1 VK² - +K

A:

Q: Evaluate.

A: Given: ∑k=14 2k-10 Substitute the value of k=1, we get  21-10=-8 Substitute the value of k=2, we get…

Q: 台(k+ 2) た=

A: Let n= 1 a(n+1)= 6/2(2+2) = 6/8 a(n)= 6/1(1+2) = 6/3 Therefore, r= lim k-&gt;inf |a(n+1)/a(n)|=…

Q: 4 k=1 k²

A: This question can be solved using the concept of summation.

Q: 4" (x-3)" /n (b) (-1)" n=1

A: INTRODUCTION: The radius of convergence is half the length of the convergence interval. If the…

Q: Σ(-1)사2(1+ k k-1

A:

Q: 1 k + 2 k=4

A:

Q: 20 6 5 Σκ b. 2 (5k + 1) E k2 а. c. k= 1 k= 1 k= 1

A:

Q: k(x) = 1- |r – 3|

A: For (b), Given: The domain of a function is the set of input or argument values for which the…

Q: M -2 3 P N Find PN 10

A: Value of PN is 15/2

Q: п п-1 п —2 What is A and B if a =A2" +B (–1)" n 3 аnd - 1 -3 аnd - 1 %3D

A: Given that:                        an=an-1+2an-2a0=2 , a1=7an=A.2n+B(-1)n

Q: Р(0 <Z < 2.17) b. Р(0 $Z < 1) а.

A: Let Z be the random variable from standard normal distribution with mean = 0 and standard deviation…

Q: \k+2

A:

Q: (a)2承+2 (b) k=1 1+ 16k²

A:

Q: 38. 32 (-1)k k=0 (2k + 1)³

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Q: 1 Σ (-3)²+" (n² + 1) -(4x – 12)" n n=0

A:

Q: 6 4. Find A: s²+4 R: r()

A:

Q: k? + k + 1 k4 + k3 + 20 k=1

A: follow next step

Q: 1 Σ 3 k=1 Z (4 + 2k)

A: The given function can be represented as, fx=14+2x32 As per the Cauchy's Integral test, the series…

Q: ○〇 k + 1 -1) 43k k=1

A:

Q: n(n + 1)(2n + 1) 6 k=0

A: In this question, we prove the sum of squares of natural numbers.

Q: b. (− 1)* k² k=1 √kº +1

A:

Q: Σ k=1 20 Τ k!

A: We will use Ratio-Test.

Q: 1 Σ (k + 2)(k + 3) k =1

A:

Q: N T (1-z-¹) 5 3 1 2 1 <2 시리<

A:

Q: a(a+1) (1-a)" α. Σ(r" (α)") - 3 n=0 .. |a|<1

A:

Q: | grk(1 – 2)n=k/(") z*(1 – 2)n-k | 2*(1 – : 1/2 1 2n/2 how did we get step 3 from step 2 ? explain…

A: First consider the second term of step 2 , which is ∑k=0nnkxk1-xn-k12 This term is in the form of…

Q: 7 > k(2k + 1) с. k=1 7 2 7 k3 d. 4 k=1 k е. k=1

A:

Q: n Σ k + 2n + n2 | n k=1

A: use the sum of first natural number  to evaluate the sum

Q: [2 1 Q2) Find B".A Where A = 3 0 and B = 6 [2 -2 1 3. 1

A: The given matrices are A=21-130-3  and  B=2-21013. Evaluate BT as follows. BT=2-21013T=20-2113

Q: Σ n+ (-1)"n n +1 (b) n=0

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: h(n)=-4n+3 g(n)=n 2 +3 Findh(-10)-g(-10)

A: Given  h(n)=-4n+3g(n)=n2+3 we need to find h(-10)-g(-10) Substitute -10 for 'n' in g(n) to find out…

Q: omplete k (-1)* 2 k! (k +n + 1)! 2k+n = -(x)

A: Given that: ∑k=1k−1kk!k+n+1!x22k+n=−J?x To determine the missing term in the above equation.

Q: (d) 2. +2 = 0 (e) In enz – 1ln r - 4 = In 3 |

A:

Q: 'n = 1 n (- 1) "xη Σ 'n = 1 n2 8. 8.

A:

Q: ди k = N k > 0

A:

Q: Σ 2n+3 + n2 +3n n-1 3.

A: Given series ∑n=1∞1n2+3n+2n+33n

Q: Σ !k² + 1 k=

A:

Q: |z+2/=1

A:

Q: 1. P(Z < 2.73)

A: The value of P(Z&lt;2.78) will be obtained using standard normal table: Procedure for finding the…

Q: 2) . (4а — 2)2n+1 n! n=0

A: Given series is ∑n=0∞4x-22n+1n!

Q: Simplify:

A: kk+12k+16+k+12

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.