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If t(r) = (r+2)/(r(r+)). 1/(2^(r+1)) th...

If `t_(r) = (r+2)/(r(r+)). 1/(2^(r+1)) ` then `sum_(r=1)^(n)` is equal to

A

`(n2^(n)-1)/(n+1)`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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FIITJEE-PROGRESSION & SERIES -ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I
  1. If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p...

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  2. Product of a G.P whose 1^(st)and last term are a and b is P. If two ...

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  3. If t(r) = (r+2)/(r(r+)). 1/(2^(r+1)) then sum(r=1)^(n) is equal to

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  4. sum(i=1)^(n) sum(i=1)^(n) i is equal to

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  5. If 1/a+1/(a-2b)+1/c+1/(c-2b)=0 and a,b,c are not in A.P., then

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  6. If the length of sides of right angled triangle are in AP, then their...

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  7. a, b, c are positive integers formaing an incresing G.P. and b-a is a ...

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  8. If the sum of an infinite G.P and the sum of the squares of its terms...

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  9. Sum of infinite series 1/(1*4)+1/(4*7)+1/(7*10)+......oo is

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  10. The sequence a1,a2,a3,a4..... satisfies a1 =1, a2 =2 and a(n+2) = 2/a(...

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  11. If (a^n+b^n)/(a^(n-1)+b^(n-1))is the A.M. between a and b, then find t...

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  12. If x(1),x(2),….x(20) are in H.P then x(1)x(2)+x(2)x(3)+….+x(19)x(20)=

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  13. If a,b,c are three positive real numbers then the minimum value of the...

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  14. If a ,b ,c are different positive real numbers such that b+c-a ,c+a-b ...

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  15. n/((n+1)!)+((n+1))/((n+2)!)+......+((n+p))/((n+p+1)!) is equal to .

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  16. The sum of two numbers is (13)/6dot An even number of arithmetic means...

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  17. The first term of an infinite G.p is 1 and any term is equal to th...

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  18. If a(1) = 2 and a(n) - a(n-1) = 2n (n ge 2), find the value of a(1) + ...

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  19. If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...

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  20. If xi>0 i=1,2,3,...50 x1+x2...+x50=50 then the minimum value of 1/(x1)...

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