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Let P(n) denote the statement that n^2+n...

Let P(n) denote the statement that `n^2+n` is odd. It is seen that `P(n) implies P(n+1)` , P(n) is true for all

A

`ngt1`

B

n

C

`ngt2`

D

None of these

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The correct Answer is:
D
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The value of the natural numbers n such that the inequality 2^ngt2n+1 ...

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  2. When P is a natural number then p^(n+1)+(p+1)^(2n-1) is divisible by

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  3. Let P(n) denote the statement that n^2+n is odd. It is seen that P(n) ...

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  4. For a positive integer n let a(n)=1+1/2+1/3+1/4+….+1/((2^n)-1) Then

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  5. Let S(k) =1+3+5+……+(2k-1)=3+k^2 Then which of the following is true:

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  6. Statement-1 for every natural number nge2 1/sqrt1 +1/sqrt2 +…..+1/sqrt...

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  7. (1+x)^n-nx-1 is divisible by (where n in N)

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  8. Statement-1 : 11^(25) +12^(25) when divided by 23 leaves the remainder...

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

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  10. The coefficient of y in the expansion of (y^2+(c/y))^5 is

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  11. The term independent of x in (x^2-(1/x))^9 is

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  12. The coefficients of x^p and x^q in the expansion of (1+x)^(p+q) are

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  13. If x^m occurs in the expansion of (x+(1/x^2))^(2n) then the coefficien...

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  14. Sum of the series 2C0+C1/2 2^2 +C2/3 2^3+………+Cn/(n+1) 2^(n+1)

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  15. The value of nC0. ^nCn +^nC1 . ^nC(n-1)++……..+^nCn . ^nC0

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  16. If (1+x)^(15)=C0+C1x+C2x^2+……..+C(15)x^(15) then ,^15C0^2-^15C1^2+^15C...

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  17. If sn= sum(r=0)^n 1/(^"nCr) and tn=sum(r=0)^n r/("^nCr) then tn/sn is ...

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  18. The fractional part of =(2^(4n))/15 is

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  19. If the fourth term in the expansion of (px+(1/x))^n is independent of ...

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  20. Find the coefficient of x^20 in the expression of (1+x^2)^40(x^2+2+1/x...

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