Series Addition
You found a super-duper great job. Every month, your boss will
increase your salary by $250. Your January salary is 5000. How
much will you earn for the first year?
Your brother found a super-duper great job. Every month, his
boss will increase his salary by 1%. His January salary is 5000.
How much will he earn for the first year?
Whose job is better?
There's a famous legend about the origin
of chess that goes like this. When the inventor of the game
showed it to the emperor of India, the emperor was so impressed
by the new game, that he said to the man "Name your reward!"
The man responded,"Oh emperor, my wishes are simple. I only wish
for this. Give me one grain of rice for the first square of the
chessboard, two grains for the next square, four for the next,
eight for the next and so on for all 64 squares, with each
square having double the number of grains as the square before."
The emperor agreed, amazed that the man had asked for such a
small reward - or so he thought. After a week, his treasurer
came back and informed him that the reward would add up to an
astronomical sum, far greater than all the rice that could
conceivably be produced in many many centuries!
How can we solve it?