Answer:
a = (1/√1) + (1/√3) + (1/√5) + ...
b = (1/√2) + (1/√4) + (1/√6) + ...
a/b = (1/√1) + (1/√3) + (1/√5) + ... / (1/√2) + (1/√4) + (1/√6) + ...
a/b = (1/√2) * [(1/√1) + (1/√3) + (1/√5) + ... ] / [(1/√2) + (1/√4) + (1/√6) + ...]
a/b = (1/√2) * [(1 + 1/√3 + 1/√5 + ...) / (1 + 1/√2 + 1/√4 + ...)]
a/b = (1/√2) * [1/(1 - 1/2)]
a/b = (1/√2) * 2
a/b = 2/√2
a/b = 2√2/2
a/b = √2
Therefore, a/b = √2.
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Answers & Comments
Answer:
a = (1/√1) + (1/√3) + (1/√5) + ...
b = (1/√2) + (1/√4) + (1/√6) + ...
a/b = (1/√1) + (1/√3) + (1/√5) + ... / (1/√2) + (1/√4) + (1/√6) + ...
a/b = (1/√2) * [(1/√1) + (1/√3) + (1/√5) + ... ] / [(1/√2) + (1/√4) + (1/√6) + ...]
a/b = (1/√2) * [(1 + 1/√3 + 1/√5 + ...) / (1 + 1/√2 + 1/√4 + ...)]
a/b = (1/√2) * [1/(1 - 1/2)]
a/b = (1/√2) * 2
a/b = 2/√2
a/b = 2√2/2
a/b = √2
Therefore, a/b = √2.