onsider the following recursively defined sequence. t = tk-1+ 3k + 1, for each integer ka 1 to - 0 he steps below begin an iterative process to guess an explicit formula for the sequence. to- 0 - to+3. 1+1=3+ 1 t2 = t, +3. 2 +1- (3 + 1) + 3:2 +1 = 3 + 3.2+2 t3 = t, +3. 3 +1- (3 + 3. 2 + 2) + 3.3 +1 = 3+3. 2 + 3:3+ 3 ontinue the iteration process in a free response. Then guess formula for t, as a summation written in expanded form, and use Theorem 5.2.1 to write it as a single fraction whose denominator is 2. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet
onsider the following recursively defined sequence. t = tk-1+ 3k + 1, for each integer ka 1 to - 0 he steps below begin an iterative process to guess an explicit formula for the sequence. to- 0 - to+3. 1+1=3+ 1 t2 = t, +3. 2 +1- (3 + 1) + 3:2 +1 = 3 + 3.2+2 t3 = t, +3. 3 +1- (3 + 3. 2 + 2) + 3.3 +1 = 3+3. 2 + 3:3+ 3 ontinue the iteration process in a free response. Then guess formula for t, as a summation written in expanded form, and use Theorem 5.2.1 to write it as a single fraction whose denominator is 2. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Consider the following recursively defined sequence.**
\( t_k = t_{k-1} + 3k + 1, \) for each integer \( k \geq 1 \)
\( t_0 = 0 \)
The steps below begin an iterative process to guess an explicit formula for the sequence.
\[
\begin{align*}
t_0 & = 0 \\
t_1 & = t_0 + 3 \cdot 1 + 1 = 3 + 1 \\
t_2 & = t_1 + 3 \cdot 2 + 1 = (3 + 1) + 3 \cdot 2 + 1 = 3 + 3 \cdot 2 + 2 \\
t_3 & = t_2 + 3 \cdot 3 + 1 = (3 + 3 \cdot 2 + 2) + 3 \cdot 3 + 1 = 3 + 3 \cdot 2 + 2 + 3 \cdot 3 + 3
\end{align*}
\]
Continue the iteration process in a free response. Then guess a formula for \( t_n \) as a summation written in expanded form, and use Theorem 5.2.1 to write it as a single fraction whose denominator is 2. (Submit a file with a maximum size of 1 MB.)
**File Upload:**
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Transcribed Image Text:**Consider the following recursively defined sequence.**
\( t_k = t_{k-1} + 3k + 1, \) for each integer \( k \geq 1 \)
\( t_0 = 0 \)
The steps below begin an iterative process to guess an explicit formula for the sequence.
\[
\begin{align*}
t_0 & = 0 \\
t_1 & = t_0 + 3 \cdot 1 + 1 = 3 + 1 \\
t_2 & = t_1 + 3 \cdot 2 + 1 = (3 + 1) + 3 \cdot 2 + 1 = 3 + 3 \cdot 2 + 2 \\
t_3 & = t_2 + 3 \cdot 3 + 1 = (3 + 3 \cdot 2 + 2) + 3 \cdot 3 + 1 = 3 + 3 \cdot 2 + 2 + 3 \cdot 3 + 3
\end{align*}
\]
Continue the iteration process in a free response. Then guess a formula for \( t_n \) as a summation written in expanded form, and use Theorem 5.2.1 to write it as a single fraction whose denominator is 2. (Submit a file with a maximum size of 1 MB.)
**File Upload:**
[Choose File] No file chosen
*Note: This answer has not been graded yet.*
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