If `1/(1+l)=v`, prove that
`v+v^(2)+v^(3)+………+v^(n)=(1-v^(n))/l`

int (1-v) (dx)) / (1 + v + v ^ (2))

The threshold frequencies for photoemission for three metals numbered 1,2,3 are respectively v_(1), v_(2), v_(3) and v_(1) gt v_(2)gt v_(3) . An incident radiation of frequency v_(0)gtv_(2) …………………cause the photoemission from 3 but…………….cause photoemission from 1.

Find the equilibrium constant for the reaction Cu^(2+)+ 1n^(2+) Cu^(+) + 1n^(3+) Given that E_(CU^(2+)//CU^(+))^(@) = 0.15V, E_(In^(2+)//1n^(+)) = -0.4V E_(1n^(3+)//1n^(+))^(@) = - 0.42V

Find 3 -dimensional vectors vec v_ (1), vec v_ (2), vec v_ (3) satisfying vec v_ (1) * vec v_ (1) = 4, vec v_ (1) * vec v_ (2) = - 2, vec v_ (1) * vec v_ (3) = 6, vec v_ (2) * vec v_ (2) = 2, vec v_ (2) * vec v_ (3) = - 5, vec v_ (3) * vec v_ (3)

(9v + 1) + (3v + 1)

(1+tan^(2)v)(1-sin v)(1+sin v)=1