I have the following summation:
And I'm tying to expand it... I'm not sure this is correct and I need help fixing it.
- i = {0, ..., 9}
- j = {1, ..., 8}
Here's my attempt:
x01 + x02 + x03 + x04 + x05 + x06 + x07 + x08 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + x23 + x24 + x25 + x26 + x27 + x28 + x34 + x35 + x36 + x37 + x38 + x45 + x46 + x47 + x48 + x56 + x57 + x58 + x67 + x68 + x78 + x10 + x20 + x30 + x40 + x50 + x60 + x70 + x80 + x21 + x31 + x41 + x51 + x61 + x71 + x81 + x32 + x42 + x52 + x62 + x72 + x82 + x43 + x53 + x63 + x73 + x83 + x54 + x64 + x74 + x84 + x65 + x75 + x85 + x76 + x86 + x87 = 2v11;
x01 + x02 + x03 + x04 + x05 + x06 + x07 + x08 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + x23 + x24 + x25 + x26 + x27 + x28 + x34 + x35 + x36 + x37 + x38 + x45 + x46 + x47 + x48 + x56 + x57 + x58 + x67 + x68 + x78 + x10 + x20 + x30 + x40 + x50 + x60 + x70 + x80 + x21 + x31 + x41 + x51 + x61 + x71 + x81 + x32 + x42 + x52 + x62 + x72 + x82 + x43 + x53 + x63 + x73 + x83 + x54 + x64 + x74 + x84 + x65 + x75 + x85 + x76 + x86 + x87 = 2v12;
x01 + x02 + x03 + x04 + x05 + x06 + x07 + x08 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + x23 + x24 + x25 + x26 + x27 + x28 + x34 + x35 + x36 + x37 + x38 + x45 + x46 + x47 + x48 + x56 + x57 + x58 + x67 + x68 + x78 + x10 + x20 + x30 + x40 + x50 + x60 + x70 + x80 + x21 + x31 + x41 + x51 + x61 + x71 + x81 + x32 + x42 + x52 + x62 + x72 + x82 + x43 + x53 + x63 + x73 + x83 + x54 + x64 + x74 + x84 + x65 + x75 + x85 + x76 + x86 + x87 = 2v13;
x01 + x02 + x03 + x04 + x05 + x06 + x07 + x08 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + x23 + x24 + x25 + x26 + x27 + x28 + x34 + x35 + x36 + x37 + x38 + x45 + x46 + x47 + x48 + x56 + x57 + x58 + x67 + x68 + x78 + x10 + x20 + x30 + x40 + x50 + x60 + x70 + x80 + x21 + x31 + x41 + x51 + x61 + x71 + x81 + x32 + x42 + x52 + x62 + x72 + x82 + x43 + x53 + x63 + x73 + x83 + x54 + x64 + x74 + x84 + x65 + x75 + x85 + x76 + x86 + x87 = 2v14;
x01 + x02 + x03 + x04 + x05 + x06 + x07 + x08 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + x23 + x24 + x25 + x26 + x27 + x28 + x34 + x35 + x36 + x37 + x38 + x45 + x46 + x47 + x48 + x56 + x57 + x58 + x67 + x68 + x78 + x10 + x20 + x30 + x40 + x50 + x60 + x70 + x80 + x21 + x31 + x41 + x51 + x61 + x71 + x81 + x32 + x42 + x52 + x62 + x72 + x82 + x43 + x53 + x63 + x73 + x83 + x54 + x64 + x74 + x84 + x65 + x75 + x85 + x76 + x86 + x87 = 2v15;
x01 + x02 + x03 + x04 + x05 + x06 + x07 + x08 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + x23 + x24 + x25 + x26 + x27 + x28 + x34 + x35 + x36 + x37 + x38 + x45 + x46 + x47 + x48 + x56 + x57 + x58 + x67 + x68 + x78 + x10 + x20 + x30 + x40 + x50 + x60 + x70 + x80 + x21 + x31 + x41 + x51 + x61 + x71 + x81 + x32 + x42 + x52 + x62 + x72 + x82 + x43 + x53 + x63 + x73 + x83 + x54 + x64 + x74 + x84 + x65 + x75 + x85 + x76 + x86 + x87 = 2v16;
x01 + x02 + x03 + x04 + x05 + x06 + x07 + x08 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + x23 + x24 + x25 + x26 + x27 + x28 + x34 + x35 + x36 + x37 + x38 + x45 + x46 + x47 + x48 + x56 + x57 + x58 + x67 + x68 + x78 + x10 + x20 + x30 + x40 + x50 + x60 + x70 + x80 + x21 + x31 + x41 + x51 + x61 + x71 + x81 + x32 + x42 + x52 + x62 + x72 + x82 + x43 + x53 + x63 + x73 + x83 + x54 + x64 + x74 + x84 + x65 + x75 + x85 + x76 + x86 + x87 = 2v17;
x01 + x02 + x03 + x04 + x05 + x06 + x07 + x08 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + x23 + x24 + x25 + x26 + x27 + x28 + x34 + x35 + x36 + x37 + x38 + x45 + x46 + x47 + x48 + x56 + x57 + x58 + x67 + x68 + x78 + x10 + x20 + x30 + x40 + x50 + x60 + x70 + x80 + x21 + x31 + x41 + x51 + x61 + x71 + x81 + x32 + x42 + x52 + x62 + x72 + x82 + x43 + x53 + x63 + x73 + x83 + x54 + x64 + x74 + x84 + x65 + x75 + x85 + x76 + x86 + x87 = 2v18;
In case you find it helpful and know how to code, the following output was generated with the following PHP snippet:
for($k = 1; $k <= 8; $k++) { $output = null; for($i = 0; $i <= 9; $i++) { for($j = 1; $j <= 8; $j++) { if($i < $j) $output .= "x$i$j + "; } } for($i = 0; $i <= 9; $i++) { for($j = 1; $j <= 8; $j++) { if($j > $i) $output .= "x$j$i + "; } } $output = substr($output, 0, strlen($output) - 3); $output .= " = 2v1$k;"; echo "$output
"; }