Question

Which summation represents the total number of pennies on the chessboard?

Answer 1

Answer:

second question answer

Step-by-step explanation:

2^64-1. option b

Answer 2

Answer:

• First option of the figure:

                                                      $\sum_{n=1}^{64}1.2^{n-1}$

Explanation:

Assume that the complete question includes the following description of how the pennies are placed on the chessboard:

"If a chessboard (8×8) were to have pennies placed on each square such that 1 penny was placed on the first square, 2 on the second, 4 on the third, and so on (doubling the number of pennies on each subsequent square), how many pennies would be on the chessboard when finished?"

From that you can write the first terms of the sequence that represent such description

Square           number of pennies         power form

   1                                 1                           1 × 2⁰

  2                                2                           1 × 2¹

  3                                4                           1 × 2²

  4                                8                          1 × 2³

  5                               16                          1 × 2⁴

  n                                                             1 × 2ⁿ⁻¹

  64                                                           1 × 2⁶³

Hence, you to have the total number of pennies you have to sum the number of pennies on every square of the chessboard, which will lead to :

1 × 2⁰ +  1 × 2¹ + 1 × 2² +  1 × 2³ +  1 × 2⁴ + ...  1 × 2ⁿ⁻¹ up to n = 64 or n - 1 = 63.

That is the sum from n = 1 to 64 - 1 of 1 × 2ⁿ⁻¹, which using summation form is the first option on the picture.

                 $\sum_{n=1}^{64}1.2^{n-1}$