Factor the difference an+1 – an to show that the given sequence {an} is strictly increasing or strictly decreasing. +00 12n +2J n=l An+1 - an = 2 strictly decreasing (12n – 2)(12n – 14)' 12 strictly increasing (12n + 2)(12n + 14) 2 ; strictly increasing (12n + 2)(12n + 14) 2 ; strictly decreasing (12n + 2)(12n + 14)' 2 strictly increasing (12n – 2)(12n + 14)

Q: (X) 16 (D) 16 (E) 256 26. The sequence A is defined by A 100 terms in sequence A? A +2 for each…

A: Given, A_1=45 and An=A_(n-1)+2. Using n=2,3,4,.. in this expression we get: A_2=47,A_3=49,A_4=51,...…

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.

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A: A sequence is a function from natural number to real numbers. It is denoted by {an} where…

Q: Use polynomial fitting to find the formula for the nth term of the sequence (an),20 which starts, 1,…

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Q: Find the limit of the sequence 14n2 – 8n – 7 1 18 – n + 7n² . - - - n=1

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Q: N + 1 aN N° + 1 is monotonic. Show that the sequence

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Q: Find the sum of1/1 · 3 +1/3 · 5 +1/5 · 7 +··· .

A: The given series is, 11.3+13.5+15.7+..... Consider the first term, 11.3=12×1-12×1+1 Consider the…

Q: Factor the difference an+1 n /too 17n + 9 Jn=1 an+1 = an = - a, to show that the given sequence {a,}…

A: Given:- n17n+9n=1+∞

Q: Factor the difference an+1 a, to show that the given sequence {a, } is strictly increasing or…

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Q: True or False: The summation 18+28+...+n8 is a polynomial of n of degree 8.

A: Given that the summation 18+28+...+n8. The objective is to check the statement " the summation…

Q: Can you use polynomial fitting to find the formula for the nth term of the sequence 4, 7, 11, 18,…

A: No. The sequence of differences is the same as the original sequence so no differences will be…

Q: X/n where n ={1,2,3,4,5,6, } find the smallest X so that you will get remainder n-1 ....

A: To find the smallest X which when divided by a set of numbers n will yield a particular remainder,…

Q: x/3+x/8+11/24

A: We have been given an algebraic expression and we need to simplify it.

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Q: Find the sum of 1, -1/2, 1/4, .... ∞. a. 3/4 b. 2/3 c. 1/7 d. 1/2

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Q: 1/3 + 1/7

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Q: Find the seventh term of the 10 expansion ( x+ y)º

A: We know that (x+y)n = ∑r=0nCrn xn-r yr Hence (x+y)10 = ∑r=010Cr10 x10-r yr

Q: Use Gauss’s trick to determine H(n) = 1 + 5 + 9 + 13 + … + (4n – 7) + (4n – 3) + (4n + 1) I'm…

A: Explained below

Q: Add. 1 and 1/4 + 1/5 * O 1 and 9/20 O 1 and 2/9 1 and 1/20 O 2/9 Subtract. 1 and 1/3 1/2 * O 2/7 O 1…

A: The detailed solution is as follows below:

Q: (n + 2)! Write down the first five terms of the sequence an %3D 8n2 + 6n + 7 d2 = dz = d4 = a5 =…

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Q: Example 18. Find the Fourier sine series in T:/3, for 0<x<T/3, f(x)= 0, for /3<x<2r/3, -7/3, for…

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