Home
Class 12
MATHS
If sum(r=1)^(r=n)(r^(4)+r^(2)+1)/(r^(4)+...

If `sum_(r=1)^(r=n)(r^(4)+r^(2)+1)/(r^(4)+r)=(675)/(26)`, then `n` equal to

A

`10`

B

`15`

C

`25`

D

`30`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `T_(e)=(r^(4)+r^(2)+1)/(r^(4)+r)=((r^(2)+r+1)(r^(2)-r+1))/(r(r+1)(r^(2)-r+1))=(r^(2)+r+1)/(r(r+1))`
`T_(r)=1+(1)/(r )-(1)/(r+1)`
`T_(1)=1+(1)/(1)-(1)/(2)`
`T_(2)=1+(1)/(2)-(1)/(3)`
`T_(3)=1+(1)/(3)-(1)/(4)`
………………..
`T_(n)=1+(1)/(n)-(1)/(n+1)`
`:.S_(n)=n+1-(1)/(n+1)=(675)/(26)`
`:.26(n+1)^(2)-26=675(n+1)`
`implies26(n+1)^(2)-675(n+1)-26=0`
`implies26(n+1)[n+1-26]+[(n+1)-26]=0`
`implies(n-25)(26n-27)=0`
`:. n=25`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise Comprehension|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|4 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

If sum_(r=0)^(n){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24) , then n is equal to (a) 3 (b) 4 (c) 5 (d) 6

Find the value of sum_(r=1)^(n) (r)/(1+r^(2)+r^(4))

The value of lim_( n to oo) sum_(r =1)^(n) (r )/(n^(2))"sec"^(2)(r^(2))/(n^(2)) is equal to -

The value of sum_(r=1)^(n+1)(sum_(k=1)^n ^kC_(r-1)) (where r, k, n in N ) is equal to

If sum_(r=0)^(n)((r+2)/(r+1)).^n C_r=(2^8-1)/6 , then n is (A) 8 (B) 4 (C) 6 (D) 5

Let P =sum_(r=1)^(50)(""^(50+r)C_(r)(2r-1))/(""^(50)C_(r)(50+r)), R = sum_(r=0)^(100)(-1)^(r) (""^(100)C_(r))^(2) The value of P - R is equal to

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of sum_(r=0)^(n)a_(r) is

The value of sum_(r=1)^(n) (-1)^(r+1)(""^(n)C_(r))/(r+1) is equal to

msum_(r=1)^n1/nsqrt((n+r)/(n-r))

If sum_(r=0)^(n){a_(r)(x-alpha+2)^(r)-b_(r)(alpha-x-1)^(r)}=0 , then