For getting upvote please send complete handwritten solution for Q4Only handwrtten accepted 1. SequenceConsider the sequence {a,}nEN where an = 2" – 3".(a) Write the first five terms of the sequence.(b) State whether the sequence appears to be (non-)increasing or (non-)decreasing.(c) Is the sequence an arithmetic progression? Explain.(d) Is the sequence a geometric progression? Explain.2. Summation(a)Write the sum 50 + 51+52+ ..+ 99 + 100 in summation notation.(b)Compute the valuethis summation.3. Weak induction in stepsLet P(n) be the following statement:1Σni(i+1)i=1n +1The following sub-problems guide you through a proof by weak induction that P(n)holds for all ne Zt.(a)In order to understand the claim, verify it by hand for n = 4.(b)the base case.What is the statement P(1)? Show that P(1) is true, which completes(c)What is the inductive hypothesis?(d)What do you need to prove in the inductive step?(e)Complete the inductive step.4. More weak inductionUse weak induction on n to prove the following claim:n! < n" for all integers n >1

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Answered: 4. More weak induction Use weak…

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4. More weak induction Use weak induction on n to prove the following claim: n! < n" for all integers n >1

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.2: Arithmetic Sequences And Partial Sums

Problem 78E

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For getting upvote please send complete handwritten solution for Q4

Only handwrtten accepted

1. Sequence
Consider the sequence {a,}nEN where an = 2" – 3".
(a) Write the first five terms of the sequence.
(b) State whether the sequence appears to be (non-)increasing or (non-)decreasing.
(c) Is the sequence an arithmetic progression? Explain.
(d) Is the sequence a geometric progression? Explain.
2. Summation
(a)
Write the sum 50 + 51+52+ ..+ 99 + 100 in summation notation.
(b)
Compute the value
this summation.
3. Weak induction in steps
Let P(n) be the following statement:
1
Σ
n
i(i+1)
i=1
n +1
The following sub-problems guide you through a proof by weak induction that P(n)
holds for all ne Zt.
(a)
In order to understand the claim, verify it by hand for n = 4.
(b)
the base case.
What is the statement P(1)? Show that P(1) is true, which completes
(c)
What is the inductive hypothesis?
(d)
What do you need to prove in the inductive step?
(e)
Complete the inductive step.
4. More weak induction
Use weak induction on n to prove the following claim:
n! < n" for all integers n >1

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