I have recently been studying the convergence of a sequence of random variables. However, Let $\left\{ X_{n}\right\} _{1}^{\infty}$ be a sequence of random variables defined on $\left(\Omega,F,P\right)$ where the range of each term $X_{n}$ is the singleton set $\left\{ 1+\frac{1}{n}\right\} .$ First, I wish to be able to find $\left\{ F_{X_{n}}\right\} _{1}^{\infty}$ and $\left\{ f_{X_{n}}\right\} _{1}^{\infty}$. Secondly, I'd like to find out whether or not
a. $\left\{ X_{n}\right\} _{1}^{\infty}$ converge in distribution
b. $\left\{ X_{n}\right\} _{1}^{\infty}$ converge in probability
c. $\left\{ X_{n}\right\} _{1}^{\infty}$ converge in almost sure sense
d. $\left\{ X_{n}\right\} _{1}^{\infty}$ converge in $p$-th moment for $p\geq1$.
I know the definitions of convergence in distribution, probability and almost sure convergence. However, I do not know what convergence in $p$-th moment mean.
Please, any help on how to begin will be appreciated. Thanks.