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The sum of n terms of the series 1+(1...

The sum of n terms of the series
`1+(1+a)+(1+a+a^(2))+(1+a+a^(2)+a^(3))+...,` is

A

`(n)/(1-a)-(a(1-a^(n)))/((1-a)^(2))`

B

`(n)/(1-a)+(a(1-a^(n)))/((1-a)^(2))`

C

`(n)/(1-a)+(a(1+a^(n)))/((1-a)^(2))`

D

`-(n)/(1-a)+(a(1-a^(n)))/((1-a)^(2))`

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-MATHEMATICAL INDUCTION -Exercise
  1. n^(th) term of the series 4+14+30+52+ .......=

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  2. 3 + 13 + 29 + 51 + 79+… to n terms =

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  3. Find the sum of the following series to n term: 1^3+3^3+5^3+7^3+ dot

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  4. If 10^(n)+3*4^(n+2) + is divisible by 9, for all ninN, then the least ...

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  5. If x^n-1 is divisible by x-k then the least positive integral value of...

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  6. If a,b are distinct rational numbers, then for all n in N the number a...

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  7. If n is an odd positive integer, then a^(n)+b^(n) is divisible by

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  8. If n is an even positive integer, then a^(n)+b^(n) is divisible by

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  9. For all n in N, (n^(5))/(5)+(n^(3))/(3)+(7n)/(15) is

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  10. The sum of n terms of the series 1+(1+a)+(1+a+a^(2))+(1+a+a^(2)+a^(...

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  11. If 3+5+9+17+33+… to n terms =2^(n+1)+n-2, then nth term of LHS, is

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  12. Using mathematical induction , to prove that 7^(2n)+2^(3n-3). 3^(...

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  13. Prove that for n in N ,10^n+3. 4^(n+2)+5 is divisible by 9 .

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  14. For each n in N, n(n+1) (2n+1) is divisible by

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  15. The sum of the cubes of three consecutive natural numbers is divisible...

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  16. ((n+2)!)/((n-1)!) is divisible by

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  17. For all n in N, n^(4) is less than

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  18. For all n in N, 1 + 1/(sqrt(2))+1/(sqrt(3))+1/(sqrt(4))++1/(sqrt(n))

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  19. For all n in N, Sigma n

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  20. For all n in N, cos theta cos 2theta cos 4theta ....cos2^(n-1)theta eq...

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