Answer
$\sum\limits_{k=1}^{\infty }{11k\text{ }}$
Work Step by Step
$11+22+33+44+\ldots $
This can be written as,
$11\cdot 1+11\cdot 2+11\cdot 3+11\cdot 4+\ldots $
This is the sum of the positive multiples of $11$, and the value of $k$ varies from $k=1$ to $k=\infty $.
Hence, it forms an infinite series.
Thus, the sigma notation is,
$\sum\limits_{k=1}^{\infty }{11k\text{ }}$
Thus, the sigma notation for the sum $11+22+33+44+\ldots $ is $\sum\limits_{k=1}^{\infty }{11k\text{ }}$.
