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The remainder, if 1+2+2^2++2^(1999) is d...

The remainder, if `1+2+2^2++2^(1999)` is divided by 5 is.

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The correct Answer is:
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`1+2+2^(2)+2^(3)+"……"+2^(1999)`
`= (1(2^(2000)-1))/(2-1)`
`= 2^(2000) - 1`
`= (1-5)^(1000) - 1`
`= 1- .^(1000)C_(1).5+.^(1000)C_(2).5^(2)+"……"+.^(1000)C_(1000).5^(1000)-1`
which is divisible by 5.
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CENGAGE-BINOMIAL THEOREM-Exercise (Numerical)
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  2. Let a and b be the coefficients of x^3 in (1+x+2x^2+3x^2)^4a n d(1+x+2...

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  3. If R is remainder when 6^(83)+8^(83) is divided by 49, then the value ...

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  4. The remainder, if 1+2+2^2++2^(1999) is divided by 5 is.

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  5. Given (1-2x+5x^2-10 x^3)(1+x)^n=1+a1x+a2x^2+ and thata1 2=2a2 then the...

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  8. The total number of different terms in the product (.^(101)C(0) - .^(1...

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  10. The value of sum(r=0)^(3) ""^(8)C(r)(""^(5)C(r+1)-""^(4)C(r)) is "".

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  11. The sum of the series (.^(101)C(1))/(.^(101)C(0)) + (2..^(101)C(2))/...

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  14. The value of lim(n rarroo) sum(r=0)^(n) (sum(r=0)^(r-1) (1)/(5^(n)).""...

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  17. The value of .^(40)C(0) xx .^(100)C(40) - .^(40)C(1) xx .^(99)C(40) + ...

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  18. The value of sum(0leiltjle5) sum(""^(5)C(j))(""^(j)C(i)) is equal to "...

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  19. If (1-x-x^(2))^(20) = sum(r=0)^(40)a(r).x^(r ), then value of a(1) + 3...

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  20. The value of 50 sum(r=1)^(49)(2r^(2) - 48r +1)/((50-r).""^(50)C(r)) is...

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