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- 3 - Use convergence test (general term test, comparison tests, intgral test etc.) to decide that which ones of the following series are convergent. I) En-1 1) Σ 2n+1 n3 5" n=1 1+n3 1 III) 0 n=2 n In n1- Use ratio or root test to determine which of the following series converge. 3" I) En=1 ôn (In n)" II) E n=1 1.3.5..(2n-1) III) E0 n=1 8" n!Given the sets: U = (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z) A = (a, e, i, o, u, y} B = [b, d, g. o, p, q) Choose the set below that represents: An B [b. d. g. p. q} 0 (0) DØ Ⓒla, e. i. u. y.
- The Martian language can be written in the familiar Roman alphabet, which has 21 consonants (B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z) and 5 vowels (A, E, I, O, U). All Martian nouns begin with a consonant, followed by one or more vowel-consonant pairs. However, no consonant can appear more than once in a single noun, and no vowel can appear more than once in a single noun. For example, VUX, DIYOK, and ZOBALUT are possible Martian nouns, but X, VUV, DIYIK, and ZEZELAL are not. How many Martian nouns are possible? Your answer must be a number. Briefly explain your answer. Recent expeditions to Mars have cast doubt on whether the Martian language can be written with exactly 21 consonants and 5 vowels. Suppose that Martian requires c consonants and v vowels, where c > 0, v > 0, and c > v. Express the number of possible Martian nouns in terms of c and v. Your answer need not be in closed form.ere be will be these id the es of Make the following pattern block pattern: yellow, green, green, red, yellow, green, green, red. a) What color will the 287th block be? Explain how you arrived at your answer. b) How many of each color block will there be when there are 254 blocks altogether? Explain how you arrived at your answer. c) How many green blocks will you have used when you place the 35th yellow block in the pattern? Explain how you arrived at your answer.If A = {vowels} and B {letters in the word “spare"}, = find: a) N{A} b) N{B} c) N(AN B) d) N(AUB)
- In how many ways can all of the letters in the word ISOSCELES be arranged if the arrangement must: a) start with E and end with E b) Have S for the middle letter c) have the vowels togrther d) have the consonants together e) ha ve the consonants and vowels alternateThere are 7 different roads between town A and town B, 4 different roads between town B and town C, and 2 different roads between town A and town C. There are 900 different possible routes between A and C. d) how many different routes are there from A to C and back that do not use any roads twice?1. How many arrangements could be made of the word GRATEFUL if: o there are no restrictions? o the first letter is a vowel and the last letter is a consonant? o the first three letters are vowels? 1. Jessie starts from home and walks three (3) blocks north and five (5) blocks east to the library. From the library, she travels four (4) blocks north and seven (7) blocks east to the pizzeria. o How many different routes can Jessie take to go from home to the library if she is always moving closer to the library? o How many different routes can Jessie take to go from home to the pizzeria if she is always moving closer to the pizzeria? 1. A teacher must select five (5) students to attend a conference. She has 11 males and 13 females to choose from. Determine the number of way of selecting: o a group of five with no restrictions o exactly 3 females o at least 4 males o at most 3 females
- 3. Find the number of words, with or without meaning, that can be formed using the letters of the word BAYANIHAN. How many of these arrangements 1) start with Y? 2) all the vowel always occur together? 3)the vowels never occur together?The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain 1. a) exactly one vowel? b) exactly two vowels? c) at least one vowel? d) at least two vowels?This Venn diagram represents areas for students who like different subjects in all combinations List all areas (in an ascending order) that represent students who like the following:(For example for students who like History you need to put 4,5,6,7 No spaces between symbols.) a) like Math only b) like English and History c) Do not like Math d) Like Math or History e) Like English and History, but do not like Math f) Like Math or English, but do not like History