Question #ca917
1 Answer
May 4, 2017
detail in explanation
Explanation:
n=1
1=1/4(5^1-1) correspond- let
n=k
1+5+5^2+5^3+...+5^(k-1)=1/4(5^k-1) is true - if
n=k+1
1+5+5^2+5^3+...+5^(k-1)+5^(k+1-1)=1/4(5^k-1)+5^k
then observe the right pattern temporarily
=>1/4*5^k+5^k-1/4
=>(5/4)*5^k-1/4
=>(1/4)*5*5^k-1/4
=>1/4*(5^(k+1)-1)
so
1+5+5^2+5^3+...+5^(k-1)+5^(k+1-1)=1/4*(5^(k+1)-1)
is also true
conclusion:
by mathematical induction ,
is true for all positive integer n