Question

How do i solve mathematical induction dealing with exponents?

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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