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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1B (BINOMIAL COEFFICIENTS)
- If n is a positive integer, then value of (3n+2)^n C0+(3n -1)^n C1 + (...
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- sum(k=1)^(oo) sum(r=0)^(k) (1)/(3^k) (""^k Cr)=
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- C2 + C4 + C6 +…..=
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- If C0, C2, C4,….. are the binomial coefficient in the expansion of (1+...
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- ""^n C0- ^n C1 + ^n C2.....(-1)^n ""^n Cn=
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- C0-2. C1+3 . C2 …..+ (-1)^n (n+1). Cn=
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- 3. C0-5. C1+ 7. C2 - 9. C3 + ….. (n+1) terms =
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- 3. ^n C0-8. ^n C1 + 13. ^n C1 - 18 , ^n C3 + ….. (n+1) terms =
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- C0 + (C1)/(2) + (C2)/(2^2) + (C3)/(2^3)+…..+(Cn)/(2^n)=
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- C1 + 4.C2 +7.C3 +…….+(3n-2).Cn=
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- C0+3. C1+5. C2 +…...(2n+1).Cn=
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- C1 + 2. C2 + 3. C3 + …... + n. Cn=
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- 2. C2 + 6. C3 + 12. C4 +….. + n (n-1) . Cn=
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- C2+2. C3 + 3. C4 + ….+ 14. C15=
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- k-^n C1 (k-1)+^n C2 (k-2)-…..+(-1)^n ""^n Cn (k-n)=
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- (C1)/(C0)+2. (C2)/(C1)+3. (C3)/(C2)+….+n.(Cn)/(C(n-1))=
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- 2.(C2)/(C1)+3.(C3)/(C2)+…...+n. (Cn)/(C(n-1))=
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- (1 +x)^15 = a0 + a1x +…..+a15 x^15 rArr sum(r = 1)^15 r (ar)/(a(r - 1)...
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- Prove that : If n is a positive integer, then prove that C(0)+(C(1))...
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- C0-(C1)/(2)+(C2)/(3)-…...+(-1)^n (Cn)/(n+1)=
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