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Find the sum up to n terms of the series...

Find the sum up to n terms of the series : `1+(6)/(7)+(11)/(49)+(16)/(343)`+....

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The correct Answer is:
`=(7^(n)-5n+4)/(7^(n-1)6)+(5(7^(n-1)-1))/(7^(n-2)36)`
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NCERT TAMIL-BINOMIAL THEOREM , SEQUENCES AND SERIES -Exercise - 5.5
  1. Find the sum up to n terms of the series : 1+(6)/(7)+(11)/(49)+(16)/(3...

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  2. Choose the correct or the most suitable answer. The value of 2+4+6...

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  3. The coefficient of x^(6) in (2+2x)^(10) is

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  4. The coefficient of x^(8)y^(12) in the expansion of (2x+3y)^(20) is

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  5. If ""^(n)C(10)gt""^(n)C(r) for all possible r , then a value of n is

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  6. If a is the arithmetic mean and g is the geometric mean of two numbers...

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  7. If (1+x^(2))^(2)(1+x)^(n)=a(0)+a(1)x+a(2)x^(2)+...+x^(n+4)and if a(0),...

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  8. If a,8 ,b are in AP,a,4b are in GP , and if a,x,b are in HP then x is

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  9. The sequence (1)/(sqrt(3)),(1)/(sqrt(3)+sqrt(2)),(1)/(sqrt(3)+2sqrt(2)...

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  10. The HM of two positive numbers whose AM and GM are 16,8 respectively i...

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  11. If S(n) denotes the sum of n terms of an AP whose common difference is...

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  12. The remainder when 38^(15) is divided by 13 is

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  13. The n^(th) term of the sequence 1,2,4,7,11,… is

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  14. The sum up to n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)...

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  15. The n^(th) term of the sequence (1)/(2),(3)/(4),(7)/(8),(15)/(16),... ...

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  16. The sum up to n terms of the series sqrt(2)+sqrt(8)+sqrt(18)+sqrt(32)+...

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  17. The value of the series (1)/(2)+(7)/(4)+(13)/(8)+(19)/(16)+.... is

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  18. The sum of an infinite GP is 18. If the first term is 6, the common rati...

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  19. The coefficient of x^(5) in the series e^(-2x) is

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  20. The value of (1)/(2!)+(1)/(4!)+(1)/(6!)+...is

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  21. The value of 1-(1)/(2)((2)/(3))+(1)/(3)((2)/(3))^(2)-(1)/(4)((2)/(3))^...

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