In general . The second addend corresponds to a geometric series. For the first one and denoting
Now you can easily find
Given S = (4/5) + (7/5^2) + (10/5^3) + ... + (31/5^10), express S in Σ form.
By considering the difference between S and (1/5)S, find S.
So this is how I did it:
S = Σ (3r+1)/5^r (Upperlimit 10, Lower limit r = 1 )
(1/5)S = Σ (3r+1)/5^(r+1)
S - (1/5)S = Σ [(3r+1)/5^r - (3r+1)/5^(r+1)]
= + 5/4 - 4/25 r = 1
+ 1/25 - 7/125 r = 2
+ 10/125 - 10/625 r = 3
+ ...
I use the method of difference to solve but there don't seem to be any terms I can cancel away... Any idea what went wrong?
THanks in advance!!