How do i solve mathematical induction dealing with exponents?

Such as: 1+7^2+7^3...7^n-1=[(7^n)-1]/6

Question

How do i solve mathematical induction dealing with exponents?

Such as: 1+7^2+7^3...7^n-1=[(7^n)-1]/6

anonymous · Answer

do you mean 1 + 7^1 + 7 ^2 ....7^n-1 ?

anonymous · Answer

yes thats equal to [(7^n)-1]/6

anonymous · Answer

prove for n=1
$$1= ((7^1)-1)/6$$
Assume true for n=k
$$1+7 + 7^2 + 7^3...+ 7^k-1 = ((7^k)-1)/6$$

prove for n=k+1

$$1+7 + 7^2...+7^k-1 +7^k = (((7^k)-1)/6) + 7^k$$
                                               $$= [(7^k)-1)+6(7^k)]/6$$
$$=[7(7^k)-1]/6$$
=[(7^(k+1))-1]/6

anonymous · Answer

true for n=1, n=k, n=k+1
therefore true for all values of n where n is a positive integer