Evaluate
A bookshelf has shelves. The top shelf has books, and each other shelf has times as many books as the shelf directly above it. If you want to read a book from the shelves, how many choices do you have?
Details and assumptions
All of the books are different.
The series is a geometric progression with and . What is the sum of the these terms?
Details and assumptions
A geometric progression is a sequence of numbers, in which each subsequent number is obtained by multiplying the previous number by a common ratio / multiple. For example, is a geometric progression with initial term 1 and common ratio 2.
Consider a geometric progression with initial term and common ratio . What is the smallest value of for which the sum of the first terms is greater than ?
Evaluate the sum to infinity: