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If an = sqrt(7+ sqrt( 7+sqrt7+ ....... )...

If `a_n = sqrt(7+ sqrt( 7+sqrt7+ ....... )))` having n radical signs then by methods of mathematical induction which is true

A

`a_(n)gt7Vnge1`

B

`a_(n)gt3Vnge1`

C

`a_(n)lt4Vle1`

D

`a_(n)lt3Vnge1`

Text Solution

Verified by Experts

The correct Answer is:
C
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MCGROW HILL PUBLICATION-MATHEMATICAL INDUCTION AND BINOMIAL THEOREM-SOLVED EXAMPLES ( LEVEL 1 Single Correct Answer Type Questions)
  1. x^(2n-1)+y^(2n-1) is divisible by x+y

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  2. For each n in N, n(n+1) (2n+1) is divisible by

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  3. If an = sqrt(7+ sqrt( 7+sqrt7+ ....... ))) having n radical signs then...

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  4. If a(n) = 2^(2^(n)) + 1, then for n > 1, last digit of a(n) is

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  5. Let S(k) = 1 + 3 + 5 +...+ (2k -1) = 3 + k^2. Then which of the follow...

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  6. Let (1 + x)^(n) = sum(r=0)^(n) C(r) x^(r) and , (C(1))/(C(0)) + 2 (...

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  7. The last term in the binomial expansion of (2^(1/3) -1/sqrt(2))^n is (...

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  8. Degree of the polynomial (x^(2)-sqrt(1-x^(3)))^(4)+(x^(2)+sqrt(1-x^(3)...

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  9. Coefficient of 1/x in the expansion of (1 + x)^(n) (1 + 1//x)^(n) is

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  10. Find the coefficient of x^4 in the expansion of (1+ x +x^2+ x^3)^11

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  11. Find the 6th term of the expansion (y^(1//2) + x^(1//3))^(n) , if the ...

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  12. If a> 0 and coefficient of x^(2),x^(3),x^(4) in the expansion of (1 + ...

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  13. The sum of the coefficients of middle terms in the expansion of (1+x)^...

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  14. If a is a real number and if the middle term of (a/3+3)^(8) is 1120, t...

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  15. Suppose F is the fractional part of M =(sqrt(13)+ sqrt(11))^(6), then ...

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  16. The remainder left out when 8^(2n)""(62)^(2n+1) is divided by 9 is (1)...

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  17. The coefficient of x^(7) in the expansion of (1-x-x^(2) + x^(3))^(6) i...

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  18. If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is ...

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  19. The coefficient of x^(n) in the expansion of (1+1/(1!)x+1/(2!)x^(2)…...

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  20. The coefficient of x^n in the expansion of (1+x)(1-x)^n is

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