Prove the following by mathematical inductionSolutionFn 145

Prove the following by mathematical induction.

F(n) = 1/4(5^n-1)

we\'ll check for F(1) = 1/4 (4)=1 which is true

We\'ll suposse F(k) is true then 1 + 5 + 52 + ……..+5k-1=1/4(5^k-1)

then F(k+1) should also be true

1 + 5 + 52 + ……..+5k-1+5k+4=1/4(5^(k+1)-1) =

1/4(5^k-1) + 5k+4 = 1/4(5^(k+1)-1)

5k+4 = 1/4(5^(k+1)-1) - 1/4(5^k-1)

5k+4= 1/4 5^k{ (4+1)}

5k+4 = 1/4 5^(k+1)

$Prove the following by mathematical induction.SolutionF(n) = 1/4(5^n-1) we\'ll check for F(1) = 1/4 (4)=1 which is true We\'ll suposse F(k) is true then 1 + 5 +$

Prove the following by mathematical inductionSolutionFn 145

Solution

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