Nevernevergiveup wrote:
What is \(\frac{1}{(1)(2)}+\frac{1}{(2)(3)}+\frac{1}{(3)(4)}+\frac{1}{(4)(5)}+\frac{1}{(5)(6)}+\frac{1}{(6)(7)}+\frac{1}{(7)(8)}+\frac{1}{(8)(9)}+\frac{1}{(9)(10)}\)?
A. \(\frac{2}{5}\)
B. \(\frac{3}{5}\)
C. \(\frac{7}{10}\)
D. \(\frac{46}{55}\)
E. \(\frac{9}{10}\)
Asked: What is \(\frac{1}{(1)(2)}+\frac{1}{(2)(3)}+\frac{1}{(3)(4)}+\frac{1}{(4)(5)}+\frac{1}{(5)(6)}+\frac{1}{(6)(7)}+\frac{1}{(7)(8)}+\frac{1}{(8)(9)}+\frac{1}{(9)(10)}\)?
1/n(n+1) = 1/n - 1/(n+1)
\(\frac{1}{(1)(2)}+\frac{1}{(2)(3)}+\frac{1}{(3)(4)}+\frac{1}{(4)(5)}+\frac{1}{(5)(6)}+\frac{1}{(6)(7)}+\frac{1}{(7)(8)}+\frac{1}{(8)(9)}+\frac{1}{(9)(10)} =\)
\(1-\frac{1}{(2)}+\frac{1}{(2)}
-\frac{1}{(3)}+\frac{1}{(3)}
-\frac{1}{(4)}+\frac{1}{(4)}
-\frac{1}{(5)}+\frac{1}{(5)}
-\frac{1}{(6)}+\frac{1}{(6)}
-\frac{1}{(7)}+\frac{1}{(7)}
-\frac{1}{(8)}+\frac{1}{(8)}
-\frac{1}{(9)}+\frac{1}{(9)}
-\frac{1}{(10)}= 1 - \frac{1}{10} = \frac{9}{10}\)
IMO E
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com