University | National University of Singapore (NUS) |
Subject | MA1301 Introductory Math |
- Do NOT upload this assignment problem set to any website.
- The assignment carries a total number of 100 marks. The marks for each question or part are as indicated.
(1) (a) [5 marks] The first term of an arithmetic sequence is 7, its last term in 70 and its sum is 385. Find the number of terms in the sequence and the common difference
(b) A geometric series is given as follows:
(i) [5 marks] Find the set of values of x such that the sum to infinity of the series exists (in other words, the series converges).
(ii) [5 marks] Find the value of x for which the sum to infinity
of the series S∞ is 43.
(c) [5 marks] An arithmetic sequence {an} ∞ n=1 of positive terms is such that twice of the sum of the first nine terms is equal to the sum of the next nine terms. Furthermore, a1, 20, a16 forms a geometric sequence. Find the first term and the common difference of the arithmetic sequence.
(2) The sum Sn of the first n terms of a sequence {ui}
∞ i=1 is given by Sn = n(2n + 2024).
(i) [5 marks] Find un in terms of n.
(ii) [5 marks] Find un+1 in terms of un.
(3) The sequence {an} is defined as follows:
a1 = 2, an+1 = 2(a1 + a2 + ⋅ ⋅ ⋅ + an) for n = 1, 2, 3 . . .
(i) [5 marks] Evaluate the numerical value of a2, a3 and a4.
(ii) [5 marks] Find the ratio of an+1
an where n ≥ 2. Is {an}∞n=2ageometric sequence?
(iii) [5 marks] Find the sum of the n terms a1 + a2 + ⋅ ⋅ ⋅ + an.
Hire a Professional Essay & Assignment Writer for completing your Academic Assessments
Native Singapore Writers Team
- 100% Plagiarism-Free Essay
- Highest Satisfaction Rate
- Free Revision
- On-Time Delivery
(5) (a) [5 marks] Let n be a positive integer with n > 1. Suppose that the coefficient of x 3 in the expansion of (1 + x) 2n and the coefficient of x 2 in the expansion of (1 + 10x) n are equal. Find the value of n.
(b) [5 marks] Let k > 0 be a constant. Suppose the coefficient of x2 in the expansion of
(6) Consider the binomial expansion (1 − x)−2
(i) [5 marks] Write down its first three terms in ascending powersof x.
(ii) [5 marks] Find the coefficient of xn.
(iii) [5 marks] Find the range of values of x for which the expansion is valid.
(iv) [5 marks] Hence, or otherwise, find the value of
∞∑n=1n2
(7) (i) [5 marks] Expand (1−x1+x)n in ascending powers of x up to and including the term in x2.
(ii) [5 marks] State the set of values of x for which the series expansion is valid.
(iii) [5 marks] Hence find an approximation to the fourth root of 19 21 , in the form p q, where p and q are positive integers with no common factors.
Stuck with a lot of homework assignments and feeling stressed ? Take professional academic assistance & Get 100% Plagiarism free papers
Facing challenges with your MA1301 Introductory Math Assignment? Let our assignment writing services assist you. Singaporean students can rely on our homework writing helper online for students, providing original content and ensuring your work is done on time. Simply ask us to do my assignment for me, and we’ll handle the rest!
Looking for Plagiarism free Answers for your college/ university Assignments.
- Financial Statement Analysis Report – Assessment 2
- COM273e Innovative Marketing Strategy for Sustainable Activewear in Asia – ECA
- NCO201 Self-Directed Learning Plan & Reflection for Personal Growth
- The impact of AEDs on OHCA Patients and Their Survival Outcomes in Singapore – Report
- MKT362 ECA – FoodPanda Case Study & Legal Compliance in Singapore
- CB0494 Predicting Lung Disease Recovery Using Data Science
- MH4522 Kernel Estimation for Poisson Point Processes – Spatial Data Science Assignment
- ANL203 Business Analytics for Student Monitoring
- Analyzing Cinematic Techniques and Themes in Film – Essay
- ELG101 Understanding Singlish and Its Cultural Significance – ECA Essay