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The sum of the first 35 terms of the series $$\frac{1}{2}$$ $$ + $$ $$\frac{1}{3}$$ $$ - $$ $$\frac{1}{4}$$ $$ - $$ $$\frac{1}{2}$$ $$ - $$ $$\frac{1}{3}$$ $$ + $$ $$\frac{1}{4}$$ $$ + $$ $$\frac{1}{2}$$ $$ + $$ $$\frac{1}{3}$$ $$ - $$ $$\frac{1}{4}$$ . . . . . is = ?
Answer & Solution
Correct Answer:
Option
B
Clearly , sum of first 6 terms is zero , So sum of first 30 terms = 0
∴ Required sum
$$\eqalign{ & {\text{ = }}\left( {\frac{1}{2} + \frac{1}{3} - \frac{1}{4} - \frac{1}{2} - \frac{1}{3}} \right) \cr & = - \frac{1}{4} \cr} $$
∴ Required sum
$$\eqalign{ & {\text{ = }}\left( {\frac{1}{2} + \frac{1}{3} - \frac{1}{4} - \frac{1}{2} - \frac{1}{3}} \right) \cr & = - \frac{1}{4} \cr} $$
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