Please could anyone help!
I need to use mathematical induction to prove that
1+5+5^2+...+5^n=1/4(5^(n+1)-1)
for all positive intergers n
Thanks
To be precise, one must define a property, not a function. If , then f(1) is neither true nor false, so one cannot prove f(1). Instead, define P(n) to be and prove P(1) and .
Why don't you post the induction hypothesis, what you need to prove and what exactly your problem is?Originally Posted by Arron
This is how far I have got,
P(1) is true, since
1+5^1=6 and 1/4(5^1+1 -1) =6
Now let k>1, and assume that P(k) is true, that is
1+5+5^2+...+5^K = 1/4(5^k+1 -).
We wish to duduce that P(k+1) is true, that is
1+5+5^2+...+5^k+1=1/4(5^K+2 -1)
Now
1+5+5^2+...+5^k+1=(1+5+5^2+...+5^k)+(5^k+1) (not sure about this line)
= (cant work out what goes here)
= 1/4(5^k+2 -1)
Hence P(K) implies P(k+1), for k=1,2....
Hence by mathematical induction, p (n) is true, for n=1,2,....