How to simply this fraction with irrational denominators? 1 1 +

pouzdrotf 2022-07-12 Answered
How to simply this fraction with irrational denominators?
1 1 + 3 + 1 3 + 5 + 1 5 + 7 1 7 + 3
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Answers (2)

Mateo Carson
Answered 2022-07-13 Author has 15 answers
If it is 1 1 + 3 + 1 3 + 5 + 1 5 + 7 + 1 7 + 3 then
= 1 1 + 3 1 3 1 3 + 1 3 + 5 3 5 3 5 + 1 5 + 7 5 7 5 7 + 1 7 + 3 7 3 7 3
= 1 3 1 3 + 3 5 3 5 + 5 7 5 7 + 7 3 7 9
= 1 3 2 + 3 5 2 + 5 7 2 + 7 3 2
= 1 2 ( 1 3 + 3 5 + 5 7 + 7 3 )
= 1 2 ( 1 3 )
= 1 2 × 2
= 1
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Raul Walker
Answered 2022-07-14 Author has 7 answers
Hint. If you rationalise the denominator of each term, you always obtain the same denominator and, in the numerator, a telescoping sum.
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