Home
Class 12
MATHS
Find the sum of n terms of the series 4...

Find the sum of n terms of the series 4/3 + 10/9+28/27+…

Text Solution

Verified by Experts

The correct Answer is:
`(3^n(2n+1)-1)/(2xx3^n)`
`4/3+10/9+28/27`+ … up to n terms
`=(1+1/3)+(1+1/9)+(1+1/27)+…`
`=n+(1/3+1/9+1/27+.." up to n terms")`
`=n+(1/3(1-1/(3^(n))))/(1-1/3)`
`=n+1/2(1-1/3^(n))`
`=n+(3^(n)-1)/(2xx3^(n))`
`=(2cdotn3^(n)+3^(n)-1)/(2xx3^(n))`
`=((2n+1)xx3^(n)-1)/(2(3^(n))`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.6|11 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.7|4 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.4|13 Videos

  • PROBABILITY II

    CENGAGE|Exercise NUMARICAL VALUE TYPE|2 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

(a)Find the sum of "n" terms of the series 2 + 4 + 6 + 8 ......

Find the sum of n terms of the series 3+7+14+24+37+………

Find the sum to n terms of the series 1 *2 *3 + 2*4*6 + 3*6*9+...

Find the sum of n terms of series : 3 + 5 + 9 + 15 + 23 + ………… n terms

Find the sum to n terms of the series sin^3 theta +1/3 sin^3 3theta+1/3^2sin^3 9theta+1/3^3 sin^3 27theta+…

Find the sum to 10 terms oif the series 1+3+6+10+…..