Hi, I have this math problem that I've been thinking... and it keeps coming back to me, so I want to solve this problem.
Say I earn $300 on the first day. $700 on the second day, $1200 on the third day.
And this goes up until 50th day.
I want to know the total sum on the 50th day.
Let f(x) be the amount of money I earn, whereas x is the day.
Σf(x=1to50)= 300 + (400+f(1)) + (500+f(2))... (5200+f(49))
Σf(x=1to50)= 300x1 + [((f(1)+100(x-1))+f(x-1))]x2 + [((f(1)+100(x-1))+f(x-1))]x3... +[((f(1)+100(x-1))+f(x-1))]x49
This is what I have so far. I could program and calculate using recursion, but I want to know if there is a way to do this quickly by hand.
Any help to this problem will be greatly appreciated.
Say I earn $300 on the first day. $700 on the second day, $1200 on the third day.
And this goes up until 50th day.
I want to know the total sum on the 50th day.
Let f(x) be the amount of money I earn, whereas x is the day.
Σf(x=1to50)= 300 + (400+f(1)) + (500+f(2))... (5200+f(49))
Σf(x=1to50)= 300x1 + [((f(1)+100(x-1))+f(x-1))]x2 + [((f(1)+100(x-1))+f(x-1))]x3... +[((f(1)+100(x-1))+f(x-1))]x49
This is what I have so far. I could program and calculate using recursion, but I want to know if there is a way to do this quickly by hand.
Any help to this problem will be greatly appreciated.
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