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Finite Sums: Sigma Notation

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Wize University Calculus 1 Textbook > Integrals

Finite Sums

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∑i=030sin⁡(iπ2)\sum_{i=0}^{30}\sin\left(\frac{i\pi}{2}\right) equals
More Finite Sums Questions:
Finite Sums
Evaluate ∑i=510[2i−3]\displaystyle\sum_{i=5}^{10}\left[2i-3\right].
Practice: Telescoping Sum (~F2017 Final Q22)
Practice: Sigma Notation
Evaluate Σi=12000 (1i+1−1i+2)\Sigma_{i=1}^{2000}\ \left(\frac{1}{i+1}-\frac{1}{i+2}\right)
Practice: Sigma Notation (~F2017 Final Q21)
Practice: Sigma Notation
Evaluate Σi=1020 (3i−4)\Sigma_{i=10}^{20}\ \left(3i-4\right).
Finite Sum with Trig
Evaluate the following sum: ∑i=25sin⁡(iπ2)\displaystyle \sum_{i=2}^{5}\sin{\left(i\frac{\pi}{2}\right)}
Finite Sum
Evaluate the following sum: ∑i=1065k(k−1)\displaystyle \sum_{i=10}^{65}k(k-1)
Finite Sum with Trig
Evaluate the sum: ∑j=120jsin⁡(jπ2)\displaystyle \sum_{j=1}^{20}j\sin{\left(j\frac{\pi}{2}\right)}
Finite Sums
Evaluate ∑i=2100 1i−1−1i\sum_{i=2}^{100}\ \frac{1}{i-1}-\frac{1}{i}.
Finite Sums
Evaluate ∑i=510[2i−3]\displaystyle\sum_{i=5}^{10}\left[2i-3\right].
Evaluate 3⋅Σi=510 [(2i)2−2(i−1)]3\cdot\Sigma_{i=5}^{10}\ \left[\left(2i\right)^2-2\left(i-1\right)\right]
Evaluate Σi=1100 (13i−1−13i)\Sigma_{i=1}^{100}\ \left(\frac{1}{3^{i-1}}-\frac{1}{3^i}\right).
Finite Sums
Evaluate
∑i=120(1+4i)\sum_{i=1}^{20}(1+4i)
The sum of the series ∑n=1N(3+∑i=1ni)=\displaystyle \sum_{n=1}^{N} {\left(3+\sum_{i=1}^n{i}\right)}=
Practice: Telescoping Sums
Evaluate ∑i=12000 (1i+1−1i+2)\displaystyle \sum_{i=1}^{2000}\ \left(\frac{1}{i+1}-\frac{1}{i+2}\right)
Practice: Sigma w/ Limits
Evaluate lim⁡n→∞ ∑i=1n(3n4)⋅[i(2i2−1)+1]\displaystyle \lim_{n\rightarrow\infty}\ \sum_{i=1}^n\left(\frac{3}{n^4}\right)\cdot\left[i\left(2i^2-1\right)+1\right]
Practice: Sigma Notation
Evaluate ∑i=1020 (3i−4)\displaystyle \sum_{i=10}^{20}\ \left(3i-4\right).
Finite Sum with Trig
Evaluate the following sum: ∑i=25sin⁡(iπ2)\displaystyle \sum_{i=2}^{5}\sin{\left(i\frac{\pi}{2}\right)}
Finite Sum
Evaluate the following sum: ∑i=1065k(k−1)\displaystyle \sum_{i=10}^{65}k(k-1)
Finite Sum with Trig
Evaluate the sum: ∑j=120jsin⁡(jπ2)\displaystyle \sum_{j=1}^{20}j\sin{\left(j\frac{\pi}{2}\right)}
Evaluate Σi=1100 (13i−1−13i)\Sigma_{i=1}^{100}\ \left(\frac{1}{3^{i-1}}-\frac{1}{3^i}\right).
Evaluate 3⋅Σi=510 [(2i)2−2(i−1)]3\cdot\Sigma_{i=5}^{10}\ \left[\left(2i\right)^2-2\left(i-1\right)\right]
Finite Sums
Evaluate Σi=310 [i(2+i)−1]\Sigma_{i=3}^{10}\ \left[i\left(2+i\right)-1\right]
Finite Sums
Evaluate Σi=11000 1ei−1ei−1\Sigma_{i=1}^{1000}\ \frac{1}{e^i}-\frac{1}{e^{i-1}}.
Finite Sums: Sigma Notation
∑i=030sin⁡(iπ2)\sum_{i=0}^{30}\sin\left(\frac{i\pi}{2}\right) equals
Practice: Sigma Notation (~F2017 Final Q21)
Practice: Sigma Notation
Evaluate Σi=1020 (3i−4)\Sigma_{i=10}^{20}\ \left(3i-4\right).
Practice: Telescoping Sum (~F2017 Final Q22)
Practice: Sigma Notation
Evaluate Σi=12000 (1i+1−1i+2)\Sigma_{i=1}^{2000}\ \left(\frac{1}{i+1}-\frac{1}{i+2}\right)