\[999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7}\]is simplified to |
A) 5997
B) 5979
C) 5994
D) 2997
Correct Answer: A
Solution :
Expression |
\[=\,\,999\frac{1}{7}+999\frac{2}{7}+....+999\frac{6}{7}\] |
\[=\,\,\left( 999+\frac{1}{7} \right)+\left( 999+\frac{2}{7} \right)+....+\left( 999+\frac{6}{7} \right)\] |
\[=\,\,(6\times 999)+\left( \frac{1}{7}+\frac{2}{7}+\frac{3}{7}+....+\frac{6}{7} \right)\] |
\[=\,\,5994+\left( \frac{1+2+3+4+5+6}{7} \right)\] |
\[=\,\,5994+\frac{21}{7}=5994+3=5997\] |
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