9000136909 Level: BSolve the equation involving binomial coefficients. \[ \left({x + 1\above 0.0pt x} \right) +\left ({x + 2\above 0.0pt x + 1}\right) = 19 \]\(8\)\(10\)\(12\)\(19\)The equation has no solution.
9000136910 Level: BSolve the equation involving binomial coefficients. \[ \left({x\above 0.0pt 0}\right) +\left ({x\above 0.0pt 1}\right) +\left ({x + 1\above 0.0pt x} \right) = 25 \]The equation has no solution.\(9\)\(1\)\(5\)\(7\)
9000136901 Level: BThe sum \(\left({15\above 0.0pt 8} \right) +\left ({15\above 0.0pt 9} \right)\) equals to:\(\left({16\above 0.0pt 9} \right)\)\(\left({15\above 0.0pt 10}\right)\)\(\left({15\above 0.0pt 7} \right)\)\(\left({16\above 0.0pt 8} \right)\)\(\left({30\above 0.0pt 17}\right)\)
9000136905 Level: BFor \(n\in \mathbb{N}\), \(n\geq 2\), the difference \(\left({n\above 0.0pt 2} \right) -\left ({ n\above 0.0pt n-2}\right)\) equals to:\(0\)\(\left (n + 2\right )\left (n + 1\right )\)\(\left({n+2\above 0.0pt n} \right)\)\(n^{2} - 1\)\(\left({n\above 0.0pt n}\right)\)
9000136903 Level: BSimplify \(\left({4\above 0.0pt 0}\right) +\left ({4\above 0.0pt 1}\right) +\left ({4\above 0.0pt 2}\right) +\left ({4\above 0.0pt 3}\right) +\left ({4\above 0.0pt 4}\right)\).\(4^{2}\)\(14\)\(\left({5\above 0.0pt 4}\right)\)\(32\)\(\left({8\above 0.0pt 4}\right)\)