The sum of the following infinite series is

$$ 2+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{8}+\frac{1}{9}+\frac{1}{16}+\frac{1}{27}+\ldots $$

In an election, the share of valid votes received by the four candidates $A, B, C$, and $D$ is represented by the pie chart shown. The total number of votes cast in the election were $1,15,000$, out of which 5,000 were invalid.

A $4 \times 4$ digital image has pixel intensities $(U)$ as shown in the figure. The number of pixels with $U \leq 4$ is:

A rectangle has a length L and a width W . where $\mathrm{L}>\mathrm{W}$. If the width, W , is increased by $10 \%$, which one of the following statements is correct for all values of L and W ?