/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 87 In an old fable, a commoner who ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q. 87 (page 825)

In an old fable, a commoner who had saved the king鈥檚 life was told he could ask the king for any just reward. Being a shrewd man, the commoner said, 鈥淎 simple wish, sire. Place one grain of wheat on the first square of a chessboard, two grains on the second square, four grains on the third square, continuing until you have filled the board. This is all I seek.鈥� Compute the total number of grains needed to do this to see why the request, seemingly simple, could not be granted. (A

chessboard consists of 8 * 8 = 64 squares.)

Short Answer

Expert verified

The total number of grains required is1.84脳1019hence the request cannot be granted

Step by step solution

01

Given information

We are given a1=1and we use the sequencean=ran-1

02

Calculate

As the number of grains on the next square is double it was on the current one we can conclude that r=2

We need to find the sum of first 64 as there are 64 boxes

hence

S64=a11-r641-rS64=1-2641-2S64=1.84脳1019

03

Conclusion

The total number of grains required is 1.84脳1019hence the request cannot be granted

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problems 61鈥�70, express each sum using summation notation.

1e+2e2+3e3+.........+nen

In Problems 71-82, find the sum of each sequence.

鈭�k=1408

In Problems 11鈥�16, evaluate each factorial expression.

3!7!4!

In Problems 29鈥�36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.

1,-2,3,-4,5,-6,...

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

a1=2;an=an-12
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.