An algebra problem by Rahil Sehgal
i = 4 ∑ 8 i 1 0 + 4 i 9 − 2 2 i 8 − 8 0 i 7 + 1 6 1 i 6 + 4 6 0 i 5 − 4 2 8 i 4 − 6 7 2 i 3 + 5 7 6 i 2 i 8 + 2 4 i 7 + 2 8 i 6 − 2 4 0 i 5 − 1 2 9 i 4 + 1 2 8 0 i 3 + 3 2 i 2 − 6 7 2 i + 5 7 6
Find the value of the above expression to about 3 decimal places.
The answer is 1.7523.
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1 solution
@Calvin Lin sir I think this problem should have a rating of Level 5
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Why? It's just a painful partial fraction summation. In fact, if you're allowed to use a calculator, you can just place the entire thing into the calculator, without having to simplify it.
There isn't any problem solving / understanding of the mathematics that is required to solve this problem.
In fact, I would prefer to delete this problem, as it is mostly a computational exercise.
: i = 4 ∑ 8 i 1 0 + 4 i 9 − 2 2 i 8 − 8 0 i 7 + 1 6 1 i 6 + 4 6 0 i 5 − 4 2 8 i 4 − 6 7 2 i 3 + 5 7 6 i 2 i 8 + 2 4 i 7 + 2 8 i 6 − 2 4 0 i 5 − 1 2 9 i 4 + 8 4 8 i 3 − 3 2 i 2 − 6 7 2 i + 5 7 6 ⇒ i = 4 ∑ 8 i 2 ( i − 1 ) 2 ( i + 2 ) 2 ( i − 3 ) 2 ( i + 4 ) 2 ( i − 1 ) 2 ( i + 2 ) 2 ( i − 3 ) 2 ( i + 4 ) 2 + i 2 ( i + 2 ) 2 ( i − 3 ) 2 ( i + 4 ) 2 − i 2 ( i − 1 ) 2 ( i − 3 ) 2 ( i + 4 ) 2 + i 2 ( i + 2 ) 2 ( i − 1 ) 2 ( i + 4 ) 2 − i 2 ( i + 2 ) 2 ( i − 1 ) 2 ( i − 3 ) 2
This gives us ⇒ ⇒ i = 4 ∑ 8 i 2 1 + ( i − 1 ) 2 1 − ( i + 2 ) 2 1 + ( i − 3 ) 2 1 − ( i + 4 ) 2 1
On simplifying, it will give the answer 1 . 7 5 2 3