Saylilbaby
  • Saylilbaby
find the sum of the following series. 14 E n=1 (2n+1) what is S10 for 1+3+9+27+...?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
you can break up the sum into 2 different sums, like this:\[\sum_{n=1}^{14}\left( 2n+1 \right)=\sum_{n=1}^{14}\left( 2n \right)+\sum_{n=1}^{14}\left( 1 \right)\]You can then further refine things: First, you can pull out any factors not involving the index (n) \[\Rightarrow \sum_{n=1}^{14}\left( 2n \right)=2\sum_{n=1}^{14}\left( n \right)\] Also, the sum of constant not involving the index is just the number of terms times the constant: \[\sum_{n=1}^{14}\left( 1 \right)= \underbrace{1+1+\cdots +1}_\text{14 terms} = 14\cdot(1)=14\] The multiplier here is 14 because we are summing 14 terms of 1.
anonymous
  • anonymous
Do you know the formula for the sum of integers?

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