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Let S(k) =1+3+5+……+(2k-1)=3+k^2 Then whi...

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

A

Principle of mathematical induction can be used to prove the formula

B

S(k)=S(k+1)

C

`S(k) = s(k+1)`

D

S(1) is correct

Text Solution

Verified by Experts

The correct Answer is:
C
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
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  3. Let S(k) =1+3+5+……+(2k-1)=3+k^2 Then which of the following is true:

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

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  5. (1+x)^n-nx-1 is divisible by (where n in N)

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

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

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

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

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

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

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

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

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

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

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

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  19. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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