SOLUTION: I am stuck can anyone assist Use the method of mathematical induction to prove that 1(5) + 2(5)^2 + 3(5)^3 + ... + n(5)^n =(5 + (4n−1)5n+1)/ 16

 + ... + 



Prove using induction, that the above is equal to





Base case:

S(1) = 5



and 









Hypothesis:

Assume 

   (*)

holds for n=k.





Now let n=k+1:





Re-writing the S(k) term using (*):

 + 



Now re-arrange (step-by-step shown):













add and subtract 





finally:





Thus (*) is true for n=k+1