(1) List the first 5 terms of oach of the soquence (a,). n+1 (d) an = sin An = 3n- - 1 3(-1)" (e) a = 3, anti = 2an - 1 nl
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A: According to our guidelines we can answer only three sub-parts and rest can be reposted.
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A: Given series is ∑n=1∞(2x+3)n2n2+n-1
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- Find x so that x - 1, x, and x + 2 are consecutive terms of ageometric sequence.Suppose that an object starts with an initial velocity of v0(in ft/sec) and moves under a constant acceleration a (in ft/sec2). Then the velocity vn (in ft/sec) after n seconds is given by vn = v0 + an. Show that this sequence is arithmetic. (Hint: Show that vn+1 − vn is constant.)For number 7, can you show why C= 3-ln4 when x=3. And can you show why the series diverges when x=5?
- The sequence fn is given as f1 = 1, f2 = 3, fn+2 = fn + fn +1 for n ≥1 How many even terms are between the first 2020 terms of that sequence?Please explain why sequence Xnk approaches +infinity and why sequence Xmk approaches -infinity. Why would one use each of the sequences if the main sequence is (n sin n)? Lastly, can I assume sequence sequence Nk sin Nk <1/2 ...therefore making it convergent? Why the other way?Find the limit inferior and limit superior of the sequence {[5 sin n]}.
- The nth term of a sequence is represented by 2n4+25n2+32n−156n4+2n3−11n2−2n+17. What is the limit of the the nth term as x becomes increasingly large?i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given by the even terms of sn and that given by the odd terms of sn both converge to 3.) Show that also limn→∞ sn = 3.ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge.
