Question

Find the sum of 10 terms of the series `1 + sqrt3 + 3` + .....

Answer 1

a = a, ar = b, ar² = c ⇒ G.P

`b/a = c/a`

`sqrt3/1 = sqrt3`

`3/sqrt3 = (sqrt3 xx sqrt3)/sqrt3`

Sn = `(a(r^n - 1))/(r - 1)`

r > 1

`S_10 = (1 xx (sqrt3)^10 - 1)/(sqrt3 - 1)`

= `(3^5 - 1)/(sqrt3 - 1)`

= `242/(sqrt3 - 1) xx (sqrt3 + 1)/(sqrt3 + 1)`

= `(242(sqrt3 + 1))/(3 - 1)`

= `(242(sqrt3 + 1))/2`

= `121(sqrt3 + 1)`