- #1
mohabitar
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So what's going on here? Since there is a 2^(k-1), I can subtract one from n and also the index? Thats what it looks like they did. Also, where did they get that 1/2 from?
mohabitar said:
So what's going on here? Since there is a 2^(k-1), I can subtract one from n and also the index? Thats what it looks like they did. Also, where did they get that 1/2 from?
mohabitar said:Oh ok..so how is it that we can change the bound? What is the rule for that or steps?
mohabitar said:But the bound for the first was n+1, so shouldn't the last term be 2^(n+1) or no?
So if my lower bound were 1, I could bring out a 2 and the new index would start from 2? And if the bound were 2, I could bring out a 4 and new bound would be 3?The 1/2=2-1 is simply the term of the summation for which k=-1; by bringing it out of the summation, the lower bound can be changed from k=-1 to k=0
mohabitar said:So if my lower bound were 1, I could bring out a 2 and the new index would start from 2? And if the bound were 2, I could bring out a 4 and new bound would be 3?
To subtract 1 from a summation, you simply subtract 1 from each term in the summation. For example, if the summation is 1+2+3+4, subtracting 1 would result in 0+1+2+3.
The purpose of subtracting 1/2 from a summation is to adjust for the starting point of the summation. By subtracting 1/2, the summation will start at 0 instead of 1, which is often more convenient for calculations.
To subtract 2^(k-1) from a summation, you can either subtract it from each term in the summation or factor it out of the summation. For example, if the summation is 2+4+6+8 and you want to subtract 2^(k-1), you could write it as 2(1+2+3+4) and then subtract 2^(k-1) from each term inside the parentheses.
Yes, you can subtract a variable from a summation as long as the variable is defined and follows the rules of summation. For example, if the summation is 3x+6x+9x and you want to subtract 2x, you would simply subtract 2x from each term to get x+4x+7x.
No, there is no specific order in which the subtraction must be done in a summation. You can subtract the numbers in any order as long as you follow the rules of summation.