SERIES Challenge 1

Algebra Level 2

Consider the following infinite series -

1 3 + 1 15 + 1 35 + 1 63 + … = a b \frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\ldots = \frac{a}{b}

If a a and b b are coprime positive integers, find a + b a+b

Hint - Find a pattern between the numbers 3,15,35.....

2 None Of These 4 5 3

Chandrashekar Giridharan by Chandrashekar Giridharan , 18, India

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1 solution

X X
May 7, 2018

1 3 + 1 15 + 1 35 + 1 63 + … = 1 2 [ ( 1 − 1 3 ) + ( 1 3 − 1 5 ) + ( 1 5 − 1 7 ) + … ] = 1 2 \frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\ldots=\frac12[(1-\frac13)+(\frac13-\frac15)+(\frac15-\frac17)+\ldots]=\frac12

1 Helpful 0 Interesting 0 Brilliant 0 Confused

That’s how I did it as well. :)

Chandrashekar Giridharan - 3 years, 1 month ago

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