1it is summation from 0 to n
-1 to the power of (n+1) x 10 ^n x 2n C n
whole divided by 81 ^n
1.Remainder when 22003 is divided by 17..
2.If n is a positive integer..
then value of
\sum_{i=0}^{n}{(-1)^{n} } 10^{n} C^{2n}_{n} divided by 81^{n}
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4 Answers
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1ans for first one is 8 we can write 22003 as 23X22000 that is 8X22000 which can be written as 8X16500=8X(17-1)500... if we expand this binomially every term is a multiple of 17 except the last which is 1 so remainder is 8X1=8 .