Please solve this, no need to solve the second image. In problem (c) the referral of A.3 is the second image. The formula for calculating the sum of all natural integers from 1 to n is well-known:n2 +nSn = 1+2+3++ n =Similary, we know about the formula for calculating the sum of the first n squares:n3n2nQn = 1.1+2·2+3· 3+... +n ·n =32Now, we reduce one of the two multipliers of each product by one to get the following sum:Mn0.1+1.2+ 2·3+3· 4++ (n – 1) · nFind an explicit formula for calculating the sum Mn. The well-known formula for calculating the sum Sn of the positive integers from 1 to n wasalready part of Problem A.3. For this problem, we consider the following rollercoaster sum:= 1.1+2.2+1·3+2·4+... +1. (n – 1) + 2· nHere, we multiple the summands successively with 1, 2, 1, 2, 1, 2, ...(a) Find an explicit formula to calculate this sumS. (Assume that n is a multiple of 2.)Now, we consider the sum S:S) = 1.1+2. 2+3·3+1·4+ 2 ·5+ 3 · 6+ ... +1· (n – 2) + 2 · (n – 1) + 3 · nHere, we multiple the summands successively with 1, 2, 3, 1, 2, 3,...(b) Again, find an explicite formula for the sum S". (Assume that n is a multiple of 3.)(c) Express S in the form ofS) = I · Sn/3 - Y ·n%3Dwhere Sn is the formula from Problem A.3 and I, Y are rational constants.(d) Find a formula for the general case of S). (That means we multiple the summandssuccessively with 1, 2, 3, ..., m, 1, 2, 3, .., m, ...; Assume that n is a multiple of m.)(e) Now, express the general formula asSm) = Im · Sn/m – Ym · Nand find explicit equations to calculate Im and Ym for a given m.т(f) Determine the growth behaviour by expressing Im and Ym with the big O notation.т

Given: Sn= 1+2+3+.......................+n = n2+n2and,Qn=1.1+2.2+3.3+...............+n.n=n33+n22+n6

The formula for calculating the sum of all natural integers from 1 to n is well-known: n² + n 2 Sn = 1+2+3+...+n= Similary, we know about the formula for calculating the sum of the first n squares: Qn1.1+2·2+3·3+...+n·n= + + n³ n² n 3 2 6 Now, we reduce one of the two multipliers of each product by one to get the following sum: Mn = 0.1+1·2+2·3+3·4+ + (n − 1). •n Find an explicit formula for calculating the sum Mn.

The formula for calculating the sum of all natural integers from 1 to n is well-known: n² + n 2 Sn = 1+2+3+...+n= Similary, we know about the formula for calculating the sum of the first n squares: Qn1.1+2·2+3·3+...+n·n= + + n³ n² n 3 2 6 Now, we reduce one of the two multipliers of each product by one to get the following sum: Mn = 0.1+1·2+2·3+3·4+ + (n − 1). •n Find an explicit formula for calculating the sum Mn.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 22EQ: 22. The networks in parts (a) and (b) of Figure 2.23 show two resistors coupled in series and in...

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