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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1B (BINOMIAL COEFFICIENTS)
- 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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- (C0)/(1) + (C2)/(3) + (C4)/(5) + ……+(C16)/(17) =
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- C0 + (C1)/(2) + (C2)/(2^2) + (C3)/(2^3)+…..+(Cn)/(2^n)=
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- C3//4+C5//6+C7//8+….=
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- C0+(C1 x)/(2)+(C2 x^2)/(3)+…...+(Cn x^n)/(n+1)=
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- 2.C0 + (2^2)/(2).C1 + (2^3)/(3).C2 + ……+(2^11)/(11).C10 =
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- k. C0 + k^2 . (C1)/(2)+k^3. (C2)/(3)+…..+ k^(n+1). (Cn)/(n+1)=
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- 2. C0+ 2^2 (C1)/(2)+2^3. (C2)/(3)+…....+2^(n+1). (Cn)/(n+1)=
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- (C0)/(2)+(C1)/(3)+(C2)/(4)+…...+(Cn)/(n+2)=
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- The sum of (n+1) terms of the series (C0)/(2)-(C1)/(3)+(C2)/(4)-(C3)/(...
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- (C0)/(2)+(C1)/(6)+(C2)/(12)+…..+ (Cn)/((n+1)(n+2))=
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