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Show that the sum of the coefficient of first `(r+1)` terms in the expansions of `(1-x)^(-n)` is `((n+1)(n+2)...(n+r))/(r!)`

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that C(1)^(2)...

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  2. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) show that (C(0))^(...

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  3. Show that the sum of the coefficient of first (r+1) terms in the expan...

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  4. Show that 4^(m)[ 1+(m)/(2)+(m(m+1))/(2*4)+(m(m+1)(m+2))/(2*4*6)+...] ...

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  5. It is given that n is an odd integer greater than 3 but n is not multi...

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  6. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n)x^(n) show that, 1^(2)*C...

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  7. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n)x^(n) show that, C(0)-2^(...

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  8. Using binomial theorem for a positive integral index, prove that (2^(3...

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  9. Find the largest coefficient in the expansion of (1+x)^(n), given that...

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  10. Given that the 4th term in the expansion of (2+(3)/(8)x)^(10) has the ...

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  11. If x in RR then find the solution set of the inquation |3x-7| gt 4.

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  12. Solve the following quadratic equation: \ x^2-(5-i)x+(18+i)=0

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  13. For every natural number n, show that 7^(2n)+2^(3n-3)*3^(n-1) is alway...

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  14. If the coefficients of the (r-1) th and (2r+3) th terms in the equatio...

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  15. If n is a positive integer then using the indentiy (1+x)^(n)=(1+x)^(3)...

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  16. If S(1), S(2), S(3),...S(n) are the sums of infinite geometric series,...

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  17. If u(r)=(1)/(r!) then show that u(0)u(n)+8u(1)+u(n-1)+8^(2)u(2)u(n-2...

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  18. a series is given by the following form : 1+(x+x^(2))+(x^(3)+x^(4)+x...

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  19. If x= cos theta+i sin theta and 1+ sqrt(1-a^(2))=na, show that, (a)/(...

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  20. Show that (a+ omega +omega ^(2))(a+omega ^(2)+omega ^(4))(a+omega ^(4)...

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