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(1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan...

`(1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2^(n) ) tan"" ((x)/( 2^n) ) =`

A

`(1)/( 2^n) cot ((x)/( 2^n) )`

B

`(1)/( 2^n) cot((x)/( 2^n) ) + cot x`

C

`(1)/( 2^n) cot ( (x)/( 2^n) ) - cot x`

D

`cot ((x)/( 2^n) ) -cot x`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. If P (n) = 1+2+3+ …. + n is a perfect square N^(2) and N is less than...

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  2. 1 + (x)/( a1) + ( x( x+a1) )/( a1 a2 ) + .... + ( x ( x+a1) (x+ a2)......

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  3. (1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2...

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  4. For any integer n ge 1, then sum(k=1)^(n) k ( k+2) is equal to

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  5. S(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^(3) and T(n) = 1+ 2 + 3+ 4….....

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  6. A = sum of first 10 natural numbers, B = sum of squares of first 10 ...

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  7. If sum (r=1)^(n) t(r) = (1)/( 12) n (n+1) (n+2) then sum(r=1)^(n) (1)...

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  8. 1+ (1+3) + (1+3+ 5) + ….n brackets =

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  9. 1+ ((1)/(3) + (1)/(3^2) ) + (( 1)/( 3^3) + (1)/( 3^4) + (1)/( 3^5) ) ...

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  10. Sum of n^( th) bracket of (1) + (2+ 3+4) + ( 5+ 6+ 7+ 8+9) + ….. is

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  11. { n (n+1) (2n+1) : n in Z} sub

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  12. If a,b and n are natural numbers then a^(2n-1) + b^(2n-1) is divisible...

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  13. If 'a' and 'b'are natural numbers such that a^(2) - b^(2) is prime num...

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  14. AA n in N, 49^(n) + 16n -1 is divisible by

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  15. AA n in , 7^(2n) + 3^(n-1) . 2^(3n-3) is divisible by

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  16. Sum of the cubes of three successive natural number is divisible by

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  17. For every natural number n, 3^(2n+2) - 8n -9 is divisible by

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  18. If 10^(n) + 3.4^(n) + x is divisible by 9 for all n in N, then least ...

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  19. AA n in N, 5^(2n+2) - 24n - 25 is divisible by

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  20. If y^(n) -1 is divisible by y+ a for all values of n in N, then a must...

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