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How many terms of the series 1+3+3^2+3^3...

How many terms of the series `1+3+3^2+3^3+3+....+3^(n-1)`must be taken to make the sum equal to 3280.

Text Solution

Verified by Experts

Let the sum of n terms of the given series be 3280
Since `S_(n) = (a(r^(n) -1))/(r-1)`
` therefore 3280 = (1(3^(n) -1))/(3-1)`
` rArr 3^(n)-1 =6560`
`rArr 3^(n) = 6562 = 3^(8)`
`therefore n = 8`
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