Question: Use mathematical induction to prove the formula for every positive integer n . 4 ( 1 + 5 + 5 2 + 5 3 ++

Use mathematical induction to prove the formula for every positive integern.

4(1+5+52+53++5n1) =5n1

FindS1

whenn= 1.

S1

=

Assume that

Sk=4(1+5+52+53++5k1) =5k1

.

Then,

Sk+1=Sk+ak+ 1= [4(1+5+52+53++5k1)] +ak+ 1.

ak+ 1=

Use the equation forak+ 1andSk

to find the equation forSk+ 1.

Sk+ 1

=

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