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Find the sum to infinity of the G.P. ...

Find the sum to infinity of the G.P.
(i) ` 2, (2)/(3), (2)/(9),….`
(ii) ` 5, - 1, (1)/(5), …`

Text Solution

Verified by Experts

(i) Here , a = 2 and ` r = (1)/(3)`
Since `|r| = |(1)/(3)| = (1)/(3) lt 1 `
We can find the sum of infinity of the given G.P.
`therefore S_(oo) = (a)/(1-r) = (2)/(1-(1)/3)`
`= 2 xx(3)/(2) = 3 `
(ii) Here ` a= 5 , r = (-1)/(5)`
Clearly `|r| = |(-1)/(5)| = (1)/(5) lt 1 `
Se can find the sum to infinity of the G.P.
`therefore S_(oo) = (a)/(1-r) = (5)/(1 + (5)/(5))`
` = 5 xx (5)/(6) = (25)/(6)`
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