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If P (n) = 1+2+3+ …. + n is a perfect s...

If `P (n) = 1+2+3+ …. + n ` is a perfect square `N^(2) and N` is less than `100`, then possible values of `n` are

A

only 1

B

1 and 8

C

only 8

D

`1, 8, 49`

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

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  4. 1 + (x)/( a1) + ( x( x+a1) )/( a1 a2 ) + .... + ( x ( x+a1) (x+ a2)......

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  5. (1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2...

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

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

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

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

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  10. 1+ (1+3) + (1+3+ 5) + ….n brackets =

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  11. 1+ ((1)/(3) + (1)/(3^2) ) + (( 1)/( 3^3) + (1)/( 3^4) + (1)/( 3^5) ) ...

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

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

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

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

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

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

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

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