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(1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) +...

`(1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2) + 3^(2) )/( 1+ 2+ 3)+ …. + n` terms =

A

`(n (n+3))/(4)`

B

`( n (n+3) )/(5)`

C

`(n ( n+2))/( 3)`

D

`(n ( n+5) )/(6)`

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. 1^(2) + 3^(2) + 5^(2) + …. upto n terms =

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  2. 2+ 3.2 + 4.2^(2) + …... upto n terms =

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  3. (1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2) + 3^(2) )/( 1...

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  4. Sum of first 'n' terms of the series = (3)/(2) + (5)/(4) + (9)/(8) + (...

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  5. 0.2 + 0.22 + 0.222+ …. upto n terms is equal to

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  6. 2+7+14+…..+ (n^(2) + 2n-1)=

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  7. 1.6 + 2.9+ 3.12+ ….. + n ( 3n+3)=

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  8. 2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

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  9. sum(n=0)^( oo) (-1)^(n) x^( n+1)=

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  10. sum(k=1)^(2n+1) (-1)^(k-1) k^2 =

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  11. cos theta + cos 2 theta + cos 3 theta + …. + cos { (n-1) theta}+ cos n...

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  12. If P (n) = 1+2+3+ …. + n is a perfect square N^(2) and N is less than...

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  13. 1 + (x)/( a1) + ( x( x+a1) )/( a1 a2 ) + .... + ( x ( x+a1) (x+ a2)......

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  14. (1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2...

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

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

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

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

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  19. 1+ (1+3) + (1+3+ 5) + ….n brackets =

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  20. 1+ ((1)/(3) + (1)/(3^2) ) + (( 1)/( 3^3) + (1)/( 3^4) + (1)/( 3^5) ) ...

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