Question

Answer 1

\(\dfrac{4\times x}{1\times5}+\dfrac{4\times x}{5\times9}+\dfrac{4\times x}{9\times13}+\dfrac{4\times x}{13\times17}=16\\ \Rightarrow x\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+\dfrac{4}{9\times13}+\dfrac{4}{13\times17}\right)=16\\ \Rightarrow x\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}\right)=16\\ \Rightarrow x\times\left(1-\dfrac{1}{17}\right)=16\\ \Rightarrow x\times\dfrac{16}{17}=16\\ \Rightarrow x=16:\dfrac{16}{17}\\ \Rightarrow x=17\)