Test 7
1.
\(\sum_{k=1}^{40}2^k=?\)
A) \(2^{41}-2\)B) \(2^{41}-1\)C) \(2^{40}-1\)D) \(2^{39}\)E) \(2^{39}-1\)
2.
\(\sum_{k=1}^{10}\left(\samefrac12\right)^{k-1}=?\)
A) \(1-2^{-9}\)B) \(2-2^{-9}\)C) \(2-2^9\)D) \(1-2^{-10}\)E) \(2-2^{-11}\)
3.
\(\sum_{k=0}^{40}(2\cdot3^k)=3^{n+1}-1\)
\(\Rightarrow n=?\)
A) \(38\)B) \(39\)C) \(40\)D) \(41\)E) \(42\)
4.
\(\sum_{k=1}^{7}4^{k+1}=?\)
A) \(2^{13}\)B) \(\samefrac{2^{11}-2}{3}\)C) \(\samefrac{2^{13}-2^3}{3}\)D) \(\samefrac{2^{20}-2^4}{3}\)E) \(\samefrac{2^{18}-2^4}{3}\)
5.
\(f(x)=\sum_{k=1}^{x}(k+2)\)
\(g(x)=\sum_{k=3}^{x}2^{k+1}\)
\(\Rightarrow(f\circ g)(4)=?\)
A) \(1106\)B) \(1176\)C) \(1224\)D) \(1272\)E) \(1306\)
6.
\(\sum_{k=1}^{21}[(-1)^{2k-3}\cdot2^{k-1}]=?\)
A) \(\samefrac{2^{21}-1}{3}\)B) \(1-2^{20}\)C) \(2^{21}-1\)D) \(\samefrac{1-2^{21}}3\)E) \(1-2^{21}\)
7.
\(\sum_{k=1}^{30}\samefrac1{k(k+1)}=?\)
A) \(930\)B) \(\samefrac{29}{30}\)C) \(\samefrac{30}{31}\)D) \(\samefrac12\)E) \(\samefrac1{930}\)
8.
\(\samefrac1{2\cdot3}+\samefrac1{3\cdot4}+\samefrac1{4\cdot5}+\cdots+\samefrac1{19\cdot20}=?\)
A) \(\samefrac{19}{20}\)B) \(\samefrac45\)C) \(\samefrac14\)D) \(\samefrac15\)E) \(\samefrac9{20}\)