If X is a geometric random variable, show analytically that P(X = n + k | X > n) = P(X = k). Using the interpretation of a geometric random variable, give a verbal argument as to why the preceding equation is true.

Taber invested money in an account where interest is compounded every year. he made no withdrawals or deposits. the function a(t)=525(1+0.05)^t represent the amount of money in the account after t years. how much money did taber origanally invested?