Taking Every Other Term

Algebra Level 3

a = 1 + 1 4 + 1 9 + 1 16 + 1 25 + a = 1+\frac 14 + \frac 19 +\frac 1{16} +\frac 1{25} + \cdots

Determine the value of the below expression in terms of a a .

1 9 + 1 25 + 1 49 + \frac 19 +\frac 1{25} +\frac 1{49} + \cdots

3 a 4 1 \frac {3a}4 -1 a 3 1 \frac a3 -1 1 + 5 a -1 + \frac 5a 5 a 1 \frac 5a -1

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2 solutions

Muhammad Maulana
Feb 7, 2016

Solution: \text {Solution:}

I too did it the same way as Muhammad Maulana but for the sake of variety here is a small trick.

Note that two options repeats twice so both of them are not the solutions since only one option is correct.

a 1.6 a \approx 1.6 ( π 2 6 ) (\frac{\pi^2}{6}) .

a 3 1 \frac{a}{3}-1 is negative ( 0.46 ) (\approx -0.46) but the required expression is a sum of positive terms leaving us with the only option 3 a 4 1 \boxed{\dfrac{3a}{4}-1}

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