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![[Post New]](/templates/default/images/icon_minipost_new.gif) 9 Apr 2007 13:17:37 IST
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(666.......6)2+(888......8) is equal to n digits n digits (A) 4/9(10n-1) (B) 4/9(102n-1) (C) 4/9(10n-1)2 (D) NOT
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9 Apr 2007 13:38:03 IST
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the answer is (4*(10^2n-1))/9 ie option b. Am i right
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9 Apr 2007 13:40:29 IST
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do it like thius .. put n = 1 we get.. 6^2 + 8 = 44 i.e. b option.... hope its clear now..(rate me)
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9 Apr 2007 14:04:28 IST
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its easy to see that (666.......6)2+(888......8) is equal to (4444....2ndigits) n-digits and thus proceed
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9 Apr 2007 17:01:44 IST
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(6666......6) = (6/9)(9999........9) = (2/3)(10n - 1)
Hence (6666......6)2 = (2/3)2(10n - 1)2
Similarly (8888.......8) = (8/9)(9999........9) = (8/9)((10n - 1)
Hence sum = (2/3)2(10n - 1)2 + (8/9)((10n - 1) = (4/9)(102n-1)
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Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur
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