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There was a sage whose name was Sissa.
he ask for grade of feet in exchange for the squares on the chess board for first square he would like to grains of beach for second he would like to multiply by itself which is full green of wheat for 3rd to must be multiplied by 4 to must be multiplied by itself 4 times and so on until the 64 square.
what is the exactly calculation of the paragraph?
and what is the solution?
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There was a sage whose name was Sissa.he ask for grade of feet in exch...
Introduction
The story of Sissa and the chessboard illustrates the concept of exponential growth. The sage requests a specific amount of grains for each square on the chessboard, leading to a staggering total.
Grain Calculation for Each Square
- Square 1: 1 grain of sand.
- Square 2: 2 grains (2^1).
- Square 3: 4 grains (2^2).
- Square 4: 8 grains (2^3).
- Square 5: 16 grains (2^4).
- ...
- Square 64: 2^63 grains.
Total Calculation
To find the total grains for all 64 squares, we sum the grains on each square:
- Total Grains = 1 + 2 + 4 + 8 + ... + 2^63.
This forms a geometric series where the first term (a) is 1, the common ratio (r) is 2, and the number of terms (n) is 64.
Formula for Geometric Series
The sum of a geometric series can be calculated using the formula:
- Sum = a * (r^n - 1) / (r - 1).
Applying this:
- Sum = 1 * (2^64 - 1) / (2 - 1) = 2^64 - 1.
Final Outcome
Thus, the total grains of wheat requested by Sissa is:
- Total Grains = 2^64 - 1 = 18,446,744,073,709,551,615 grains.
This number is astronomically large, demonstrating the power of exponential growth. The tale serves as a profound lesson about the nature of infinity and resource allocation.
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There was a sage whose name was Sissa.he ask for grade of feet in exchange for the squares on the chess board for first square he would like to grains of beach for second he would like to multiply by itself which is full green of wheat for 3rd to must be multiplied by 4 to must be multiplied by itself 4 times and so on until the 64 square. what is the exactly calculation of the paragraph? and what is the solution?
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