astroroman
Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

In the top row of an chessboard, Tom writes the values 1, 2, 4, 8, 16, 32, 64, 128. In the leftmost column, Tom writes the values 1, 3, 9, 27, 81, 243, 729, 2187. In every other square that doesn't have a number yet, Tom writes the product of the leftmost number in that square's row and the topmost number in that square's column. What is the sum of all the numbers on the chessboard?


Sagot :

kate200468
[tex]sum\ of\ the\ values\ in\ the\ top\ row:\\\\S=1+2+4+8+16+32+64+128= \frac{1-2^8}{1-2} =2^8-1=255\\\\ the\ sum\ of\ all\ the\ numbers\ on\ the\ chessboard:\\\\S\cdot1+S\cdot3+S\cdot9+S\cdot27+S\cdot81+S\cdot243+S\cdot729+S\cdot2187=\\\\=S\cdot(1+3+9+27+81+243+729+2187)=255\cdot \frac{1-3^8}{1-3} =\\\\=255\cdot \frac{-6560}{-2} =255\cdot3280=836,400\\\\Ans.\ the\ sum\ of\ all\ the\ numbers\ on\ the\ chessboard\ is\ 836,400[/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.