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Prove that 1+(1+x)+(1+x+x^(2))+(1+x+x^...

Prove that
`1+(1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+...+` to n terms `=(n)/(1-x)-(x(1-x^(n)))/(1-x)^(2)`

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. Prove that any sequence of numbers a(1),a(2),...a(n) satisfying the co...

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  2. If (a-bx)/(a+bx)=(b-cx)/(b+cx)=(c-dx)/(c+dx) show that a,b,c , d are i...

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  3. Prove that 1+(1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+...+ to n terms =(n...

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  4. Show that in A.P. the sum of two terms equidistant from the begining a...

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  5. If there be m quantities in a G.P. whose common ratio is r and S(m)den...

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  6. If a,b,c are in G.P. are log(c) a , log (b) c, log(a) b are in A.P. , ...

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  7. Find the sum to n terms of the following series. 5+555+55555+...

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  8. If x in RR, solve the inequation (5x+8)/(4-x) lt2

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  9. The population of a twon at the beginning of a year is N and the figur...

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  10. Examine the validity of the following statement: If a and b ar odd i...

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  11. Show that the total number of permutations of n diferent things not mo...

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  12. A and B stand in a line with 10 other people. In how many of the perm...

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  13. Find the number of permutations of the letters x,x,x,y,y,y,z,w taken 5...

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  14. A bag contains 50 tickets 1,2,3,...50 of which 5 are drawn at random a...

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  15. In n gt 7 prove that ""^(n-1)C(3)+""^(n-1)C(4) gt ""^(n)C(3)

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  16. If (""^(n)C(r-1))/(a)=(""^(n)C(r))/(b)=(""^(n)C(r))/(c) prove that n=(...

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  17. A,B and C have respectively 4,3 and 2 differrent books. In how many d...

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  18. Find the modulus and ampltidue of the complex in numberz=(-2-i2 sqrt(3...

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  19. Find the amplitude of z=1+i "tan" (3pi)/(5)

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  20. Find the modulus and amplitude of z="sin" (6pi)/(5)+I (1+"cos" (6pi)...

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