Home
Class 12
MATHS
For the series, S=1+1/((1+3))(1+2)^2+1/(...

For the series, `S=1+1/((1+3))(1+2)^2+1/((1+3+5))(1+2+3)^2+1/((1+3+5+7))(1+2+3+4)^2` +... 7th term is 16 7th term is 18 Sum of first 10 terms is `(505)/4` Sum of first 10 terms is `(45)/4`

A

7th term is 16

B

7th term is 18

C

sum of first 10 terms is `(505)/(4)`

D

sum of first 10 terms is `(405)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`:.S=1+(1)/(1+3)(1+2)^(2)+(1)/(1+3+5)(1+2+3)^(2)+"......."`
`T_(n)=(1)/(1+3+5+7+"........"" n terms ")*(1+2+3+"......."" n terms " )^(2)`
`=(1)/([(n)/(2)[2*1+(n-1)*2]])*((n(n+1))/(2))^(2)=((n+1)^(2))/(4)`
(a) `T_(7)=((7+1)^(2))/(4)=(64)/(4)=16`
(b) `S_(10)sum_(n=1)^(10)((n+1)/(2))^(2)=(1)/(4)sum_(n=1)^(10)(n^(2)+2n+1)`
`=(1)/(4)(sum_(n=1)^(10)n^(2)+2sum_(n=1)^(10)n+sum_(n=1)^(10)1)`
`=(1)/(4)((10xx11xx21)/(6)+(2xx10xx11)/(2)+10)`
`=(1)/(4)(385+110+10)=(505)/(4)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|24 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

For the series S=1+(1)/((1+3))(1+2)^(2)+(1)/((1+3+5))(1+2+3)^(2)+(1)/((1+3+5+7))(1+2+3+4)^(2)+…………….., if the 7^("th") term is K, then (K)/(4) is equal to

If the 10^(th) term of an A.P. is 1/5 and its 20^(th) term is 1/3 , then the sum of its first 150 terms is:

Sum to n terms the series 1 + (1+ 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4).......

Find the sum to n terms of the series: 1/(1. 3)+1/(3. 5)+1/(5. 7)+

If the r^(th) term of a series is 1 + x + x^2 + .......+ x^(r-1) , then the sum of the first n terms is

The sum of the series : 1 + (1)/(1 + 2) + (1)/(1 + 2 + 3)+ .... up to 10 terms, is

Sum of infinite terms of series 3 + 5. 1/4 + 7. 1/4^2 + .... is

The sum to n terms of [(1)/(1.3)+(2)/(1.3.5)+(3)/(1.3.5.7)+(4)/(1.3.5.7.9)+…………]

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1 + 2/3 + 4/9 +dotdotdot

Sum to n terms of the series 1^(3) - (1.5)^(3) +2^(3)-(2.5)^(3) +…. is