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March 16th, 2019, 12:25 AM   #1
VKN
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Thumbs up can anyone help me with? FUNCTIONS?!

If f(x) satisfies f(x+y) = f(x) + f(y) for all x,y belonging to $\mathbb{R}$, and f(1) = 5, find
$\!$ m
$\displaystyle \sum$ [f(n)]
n=1

Last edited by skipjack; March 16th, 2019 at 03:09 AM.
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March 16th, 2019, 03:11 AM   #2
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Using x = y = 1, f(2) = f(1) + f(1) = 10. You can similarly calculate f(3), f(4), etc. Does that help?
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April 18th, 2019, 08:58 PM   #3
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Well if we say $\displaystyle f(1)=5, f(2)=10$ since $\displaystyle f(2)=f(1+1)=f(1)+f(1)=5+5$ and continuing with this, we see that we get the sequence 5, 10, 15, 20, 25 etc. Summing over these up to the mth term, you can use the standard formula:

$\displaystyle S_m=\frac{m}{2}[2a+(m-1)d]$ where $\displaystyle a=d=5$
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