Question
\(\left(1-\frac{1}{n}\right)+\left(1-\frac{2}{n}\right)+\left(1-\frac{3}{n}\right)+... up to n terms = ?\)
Answer: Option C
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\(\left(1-\frac{1}{n}\right)+\left(1-\frac{2}{n}\right)+\left(1-\frac{3}{n}\right)+... up to n terms \)
= \(\left(1+1+1+... up to rerms \right) - \left(\frac{1}{n}+\frac{2}{n}+\frac{3}{n}+...up to rerms\right)\)
= \(n-\frac{1}{n}\left(1+2+3+...up to rerms\right)\)
= \(n-\frac{1}{n}\left[\frac{n(n+1)}{2}\right]\)
= \(n-\frac{(n+1)}{2}\)
= \(\frac{(2n-n-1)}{2}\)
= \(\frac{n-1}{2}\)
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