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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

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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))`
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