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Precalculus Mathematics Homework Help
Changing the Limits of Summation
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[QUOTE="ShayanJ, post: 4963669, member: 160907"] So we have the sum [itex] \displaystyle \sum_{r=m}^n T_r [/itex]. We may change the index of summation from r to s=r+k. Then because r starts from m, s should start from m+k and because r ends at n, s should end at n+k. This means that we changed our summation to [itex] \displaystyle \sum_{s=m+k}^{n+k}T_{s-k} [/itex]. But you should note that this sum doesn't depend on s as the first sum didn't depend on r. r and s are just dummy indices because after you do the sums, there'll remain no sign of them. So I can safely rename s to r. But because the sums are just numbers and because the changes I did to the first sum doesn't change the result, I'll have: [itex] \displaystyle \sum_{r=m}^n T_r=\sum_{r=m+k}^{n+k}T_{r-k} [/itex]. [/QUOTE]
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Precalculus Mathematics Homework Help
Changing the Limits of Summation
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