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Bonus Knowledge
To solve the equation
, let’s start by calculating the sum explicitly. The expression inside the summation can be rearranged:
is a linear function. When we sum from
to
, we can calculate the sum of the first few terms and then use the formula for the sum of an arithmetic series.
Now, the sum can be split:
. The first part simplifies to
since we’re summing the constant 2 for
terms. The second part calculates to
. By equating this to -7085 and solving for
, we find the largest integer that will satisfy the initial summation equation.
Remember to check for integer values of
that could possibly yield a correct calculation as this sum is defined for integer inputs only! Use consistent checks and simple arithmetic to avoid common mistakes in these equations.
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