Answer: 2^1000
Which is approximately 1.0715 * 10^301
Step-by-step explanation
The theorem is that "The sum of all of the values in row n of Pascal's Triangle is 2^n"
- For instance, in row 4 we have the values: 1, 4, 6, 4, 1. They add to 1+4+6+4+1 = 16 and notice how 2^4 = 16.
- Another example: Lets add up the values in row 5 to get 1+5+10+10+5+1 = 32 and notice how 2^5 = 32.
- Last example: add up the values in row 6 to get 1+6+15+20+15+6+1 = 64 and 2^6 = 64.
Put another way: the sum of any row is twice that of the previous row sum.
The number 2^1000 is so very big it's best to keep it in that format. But if you want you can convert it to the scientific notation of roughly 1.0715 * 10^301
To expand this to a standard number, move the decimal point in 1.0715 exactly 301 spaces to the right. You'll get a very massive number. It will start with 10715 and the have 297 zeros after it (since 301-4 = 297 and 4 is the number of decimal digits in 1.0715)