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March 16th, 2019, 12:25 AM  #1 
Newbie Joined: Mar 2019 From: India Posts: 1 Thanks: 0  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. 
March 16th, 2019, 03:11 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,937 Thanks: 2210 
Using x = y = 1, f(2) = f(1) + f(1) = 10. You can similarly calculate f(3), f(4), etc. Does that help?

April 18th, 2019, 08:58 PM  #3 
Newbie Joined: Apr 2019 From: Europe Posts: 3 Thanks: 0 
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: $\displaystyle S_m=\frac{m}{2}[2a+(m1)d]$ where $\displaystyle a=d=5$ 

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