Test 20
1.
\(A=\sum_{k=-5}^{5}k^3\)
\(B=\sum_{k=-4}^{0}2^{-k}\)
\(\Rightarrow A+B=?\)
A) \(-64\)B) \(-48\)C) \(-32\)D) \(15\)E) \(31\)
2.
\(\sum_{k=-5}^{6}(k^3+k)=?\)
A) \(222\)B) \(216\)C) \(42\)D) \(36\)E) \(0\)
3.
\(\sum_{k=-6}^{6}(k^3-3k^2+3k-1)=?\)
A) \(-559\)B) \(-343\)C) \(-216\)D) \(216\)E) \(343\)
4.
\(\prod_{k=1}^{180}\sin(k^\circ)=?\)
A) \(-1\)B) \(-\samefrac12\)C) \(0\)D) \(\samefrac12\)E) \(1\)
5.
\(\prod_{x=1}^{180}(\cos x^\circ-\sin x^\circ)=?\)
A) \(-1\)B) \(-\samefrac12\)C) \(0\)D) \(\samefrac12\)E) \(1\)
6.
Which expression represents
\((1\cdot3)(2\cdot4)(3\cdot5)\cdots(24\cdot26)?\)
A) \(\prod_{k=1}^{25}(k^2+k)\)B) \(\prod_{k=1}^{24}k(k+2)\)C) \(\prod_{k=2}^{25}(k^2+1)\)D) \(\prod_{k=2}^{25}(k^2-4)\)E) \(\prod_{k=1}^{24}(3k^2-3k)\)
7.
\(K=\underbrace{\sum_{t=1}^{10}\sum_{t=1}^{10}\cdots\sum_{t=1}^{10}}_{10\text{ times}}10\)
\(\Rightarrow K=?\)
A) \(10\)B) \(100\)C) \(10^9\)D) \(10^{10}\)E) \(10^{11}\)
8.
\(\samefrac{\prod_{k=1}^{n}(k+2)}{\prod_{i=1}^{n}(i+1)}=49\)
\(\Rightarrow n=?\)
A) \(100\)B) \(98\)C) \(96\)D) \(94\)E) \(92\)