For a n as follows, write the sum as a geometric series of the form ∑ n = 1 ∞ a r n . State whether the series converges and if it does, find the value of ∑ a n . 95. a 1 = 10 and a n / a n + 1 = 10 for n ≥ 1
For a n as follows, write the sum as a geometric series of the form ∑ n = 1 ∞ a r n . State whether the series converges and if it does, find the value of ∑ a n . 95. a 1 = 10 and a n / a n + 1 = 10 for n ≥ 1
For
a
n
as follows, write the sum as a geometric series of the form
∑
n
=
1
∞
a
r
n
. State whether the series converges and if it does, find the value of
∑
a
n
.
Refer to page 100 for problems on graph theory and linear algebra.
Instructions:
•
Analyze the adjacency matrix of a given graph to find its eigenvalues and eigenvectors.
• Interpret the eigenvalues in the context of graph properties like connectivity or clustering.
Discuss applications of spectral graph theory in network analysis.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]
Refer to page 110 for problems on optimization.
Instructions:
Given a loss function, analyze its critical points to identify minima and maxima.
• Discuss the role of gradient descent in finding the optimal solution.
.
Compare convex and non-convex functions and their implications for optimization.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]
Refer to page 140 for problems on infinite sets.
Instructions:
• Compare the cardinalities of given sets and classify them as finite, countable, or uncountable.
•
Prove or disprove the equivalence of two sets using bijections.
• Discuss the implications of Cantor's theorem on real-world computation.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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