Plz complete it will definitely upvote Consider the following family of series, one for each constant p > 0:S(p) =n=2For each N > 2 we define the partial sum up to index N and the corresponding remainder as follows:1n=2 n(logn)p¹(a) Express the following definite integral in terms of a, b, and p (assume a > 1):dxS. (log z)PSN (P) =1n(logn)∞a1 ==Use p = 2.8 in all parts below. Please enter your answers in calculator ready form.(b) Express the following definite integral in terms of a (assume a > 1):dxzloga) 28RN (P) SSN (P).S(2.8) ==In(b)^(1-p)/(1-p)-In(a)^(1-p)/(1-P)=(c) The integral test provides a two-sided inequality of the following form for RN (2.8) when N = 45:dxSo · ≤ R$45 (2.8) ≤ 0x(log x) 2.8441Find the integers a₁ and a2 above. (Use the smallest compatible value of a₁ and the largest compatible value of a 2.)1/(1.8ln^(1.8)(a))a2 =dx(log z) 2.8(d) Computation reveals S45 (2.8) = 1.966426. Use this fact, together with your earlier work, to complete this two-sided inequality involving the exact value of the series S(2.8):

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Consider the following family of series, one for each constant p > 0: 1 n(logn) S(p) = For each N > 2 we define the partial sum up to index N and the corresponding remainder as follows: SN (P) = N 1 n(logn)P (a) Express the following definite integral in terms of a, b, and p (assume a > 1): dx Sº x(log x) P RN(P) SSN(p). = a1 In(b)^(1-p)/(1-p)-In(a)^(1-p)/(1-P) Use p = 2.8 in all parts below. Please enter your answers in calculator ready form. (b) Express the following definite integral in terms of a (assume a > 1): Soz dx 1/(1.8ln^(1.8)(a)) x(log x) 2.8 (c) The integral test provides a two-sided inequality of the following form for RN (2.8) when N = 45: DO da < R4s (2.8) ≤2(log 2)2.8 用 Soz dx x(log x) 2.8 Find the integers a₁ and a₂ above. (Use the smallest compatible value of a₁ and the largest compatible value of a 2.) a2