# Calculus

Legend has it that long ago a kind was very pleased with the game of chess that he decided to reward the inventor of the game Anna, with whatever she wanted. Anna asked for a resource instead of money. Specifically, she asked for one grain of wheat for the first square of a chessboard, two grains of wheat for the second square, four grains of wheat for the third square, and so on until the entire chess board was full. There are 64 squares on a chess board)

What would be an expression for the total amount of grain needed to fulfill Anna's request.

1. 👍 0
2. 👎 0
3. 👁 229
1. clearly
1+2+4+8+ ... + for 64 terms
a GS, where a=1, r=2 and n=64

sum(64) = 1(2^64 - 1)/(2-1)
= 2^64 - 1

notice for this series
sum(2) = 3 = 2^2 - 1
sum(3) = 7 = 2^3 - 1
sum(4) = 15 = 2^4 - 1
...
sum(64) = 2^64 - 1

1. 👍 0
2. 👎 0
2. 2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
say you had three squares. labeled 1, 2 and 3
the first square has 2^0 = 1
the second square has 2^1 = 2
the third square has 2^2 = 4
now go on to 64 th square has 2^63
now 2^63 = approximately 9.33 * 10^18

1. 👍 0
2. 👎 0
3. I gave you the amount on the last square. Use Reiny's system.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### English

1. He beat me at chess. 2. He won me at chess. 3. He beat the tennis game. 4. He won the tennis game. (Which ones are grammatical? Would you let me know the differenbe between 'beat' and win'?)

2. ### English

The author's purpose is to inform the reader. Which statement best demonstrates this intent? a. a verdant rain-forest rises out of the ocean to snow capped peaks. b. Scholars are not sure about the legend but do speculate that the

3. ### LA

The following questions are from "science and the Sense of Wonder" by Asimov 1. (Part A) What is Asimovs main idea in the essay? a. Space is best apprecieated through poetry b. Poetry and science can work together c. the universe

4. ### Technology

Which of the following is one way to assess whether or not a learning game is effective? A.Being able to win the game B.Doing the quiz before and after the game to see what you have learned.*** C.Making it difficult to win the

1. ### Math

Challenger elementary school has 800 students every Wednesday 12% of the students stay after school for chess club how many students attend chess club on Wednesdays

2. ### math

in a school half of students play badminton 1/4 play volleyball 1/8 play tennis 1/16 play chess and remaining go for swimming if the number of students playing volleyball is 160 how many students play chess?

3. ### math

ok this is in my practice book. there are 33 students in the chess club. there are five more boys than girls in the club. write and solve a system of equations to find the number of boys and girls in the chess club?

List and briefly outline the six different periods into which the Paleozoic era is divided. The six periods: 1:Cambrian, which was 545 million years ago. 2:Ordovician, which was 490 million years ago. 3:Silurian, which was 445

1. ### History

Which most accurately describes the beginnings of the Islam religion? according to legend, Jesus of Nazareth was born in Bethlehem as the son of god guru Nanak was the founder of Islam, which follows the teaching of the guru