For every positive integer n     12+22+32+...+n2=n(n+1)(2n+1)/6 Let S(n)=12+22+32+...+n2 How do you get the basic and inductive step

Q: 32-2n Σ=3 Ln=3_25-n

A: We have to evaluate ∑n=3∞ 32-2n25-n.

Q: Given this example: n-1 i. E(n – k)2* Answer for (c.i): 2"+1 – 2 – n k=0 If S is the sum, then 2S –…

A:

Q: 3n > n for every positive integer n.

A: Now, since we assumed 3k>k, we can substitute k with 3k in the inequality: 3k+1>3k Since ,…

Q: 20x + 20y = 80X20-3 3. Rajah di sebelah menunjukkan susunan gambar di dalam sebuah bingkai gambar.…

A: The distance between the pictures is 2 cm and the distance between the picture and the edge of the…

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

A:

Q: (a) For every integer n, the number n² — n must be even. (b) For all real numbers a, a² < a¹. (c)…

A:

Q: the statement below true or false for n=1? ©George Mason University 2+ 4 + 6+ ... + 2n = n² + n + 1

A:

Q: 1+ x Σ Aa" (1 – 2)? n=0

A:

Q: If all tems except ys of the sequence Y1» Y2» Y3. Y9 be given , show that the value of ys is 56 (y4…

A:

Q: (-i)a is e(1+4n)i wheren is an integer. where n is an integer. O equal to the above O equal to the…

A: Any complex number, z can be written in the form of  z=reiθ . The complex number i can be written as…

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: Express the sum 3 + 5 + 7+ ... + (2k-1) using E-notation.

A: The given sum is 3+5+7+…+2k-1. Express the sum 3+5+7+…+2k-1 using ∑ notation as follows.

Q: Q1 (b): If Xi= 1,3,5,7,9,11 and Yi= 0,2,4,6,8,10. The values of the :following term is i=n 2n – 3…

A: Given,∑i=1i=n2n-3πyi-11+xii-1here n=6

Q: +6n +3 is Θ (n)

A: 1st expression is TRUE

Q: (6.1) Prove if r is a positive, even integer then 10* – 1 is divisible by 11. (6.2) Prove if r is a…

A:

Q: 3. Find |S| for S = {n|(n+1)n² − 4(n+1)=0}

A:

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: M² Prove by M I that 1+4+9+ ·· +n³²= £m(n+1)(2n+1)

A: we have to prove that 1+4+9+...+n2=n(n+1)(2n+1)6

Q: If A=-1 4 -3 -7/ -1 and A¹=/? ? (22 a ? What is the value of the element a? Give your answer…

A:

Q: Prove that 2n + 3n is a multiple of 5 for all odd n € N.

A:

Q: Find the sum of 1/7 + 3/7 + 32/7 + 32 /7 + ⋅⋅⋅ + (3)n-1 / 7

A:

Q: Show that n*-n3.5+300n + 234n²log n³ + nVn10 e 0(n*)

A:

Q: If the sum 5+ 5(3)+5(3)² +...+5(9)* =5465 then the value of k is (a) 5 (b) 6 (c) 3 (d) 4

A: We know that 1+a+a2+a3+…+an-1=an-1a-1, if a≠1

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

A:

Q: /3 n" +n + 10 8WE

A:

Q: Find the sum 1 9k2 + 12k – 5 k=1 Express your answer as a rational expression in terms of n.

A:

Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: m*n-s for m = -3 and n = 2

A: Our objective is to find the solution

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.