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Prove by induction that the integer next...

Prove by induction that the integer next greater than `(3+sqrt(5))^n` is divisible by `2^n` for all `n in N`.

A

`2^(n-1)`

B

`2^(n+1)`

C

`2^(n+2)`

D

not divisible by 2

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The correct Answer is:
B
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DISHA PUBLICATION-BINOMIAL THEOREM -EXERCISE-1 (CONCEPT BUILDER )
  1. The number of real negavitve terms in the binomial expansion of (1 ...

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  2. The numberof integral termsin the expansion of (qrt(3)-root(8)(5))^256...

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  3. Prove by induction that the integer next greater than (3+sqrt(5))^n is...

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  4. The value of x in the expression (x+x^((log)(10)))^5 if third term in ...

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  5. If the 6th term in the expansion of [1/x^(8/3)+x^2 log10 x]^8 is 5600...

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  6. The sum of the rational terms in the binomial expansion of (2^((1)/(2)...

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  7. If the 7th tern in the binomial expansion of (3/((84)^(1/3)) +sqrt(3) ...

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  8. The sum of the coefficients in the expansion of (x^(2)- (1)/( 3))^(199...

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  9. The value of .^(20)C(10)+.^(20)C(1)+.^(20)C(2)+.^(20)C(3)+.^(20)C(4)+....

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  10. If the coefficient of x^7in[a x^2-(1/(b x^2))]^(11) equal the coeffici...

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  11. The sum of the series C 20()0-C 20()1+C 20()2-C 20()3+...-...+C 20()(1...

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  12. The sum of the series (12)/(2!)+(28)/(3!)+ (50)/(4!) + ( 78)/(5!)+"......

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  13. The coefficient of x^(53) in the expansion sum(m=0)^(100)^(100)Cm(x-3)...

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  14. The ratio of the coefficient of x^(15) to the term independent of x in...

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  15. (C0)/1+(C2)/3+(C4)/5+(C6)/7+.....=

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  16. Consider the expansion of (1 + x)^(2n+1) If the coefficients of x^(r...

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  17. The value of ""^(50)C(4)+sum(r=1)^(6)""^(56-r)C(3), is

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  18. If x is very small in magnitude compared with a such that ((a)/(a+ ...

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  19. In the expression (x+1) (x+4)(x+9)(x+16)"….."(x+400), the coefficient ...

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  20. (C(1))/(C(0))+(2.C(2))/(C(1))+(3.C(3))/(C(2))+ . . .+(20.C(20))/(C(19)...

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