Notations:: $H^i_I(M)$ is $i^{th}$ local cohomology of $M$ with support in $I$ and $H^i_I(M)=R^i\Gamma_I(M)$ where $R^i\Gamma_I(M)$ is the right derived functor of a covariant left exact functor, where $\Gamma_I(M)=\{m\in M \mid I^nm=0 \text{ for some }n\}$.
Suppose every element of $M$ is killed by a power of $I$.
Claim:: $H^0_I(M)$ = $M$ and $H^i_I(M)=0$ for $i > 0$.
$H^0_I(M)$ = $M$ is clear from definition
Please do not assume direct limit definition of local cohomology
Local Cohomology An Algebraic Introduction with Geometric Applications by BRODMANN -SHARP
