What is the sum of
$$1\frac{1}{2}+4\frac{1}{6}+7\frac{1}{12}+10\frac{1}{20}$$.......... upto 20 terms?

$$1\frac{1}{2}+4\frac{1}{6}+7\frac{1}{12}+10\frac{1}{20}..........upto\ \ 20\ \ terms.$$

Or ,we can rewrite it as :

$$\left(1+4+7+10+.....+58\right)+\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{420}\right)$$

$$=\frac{20}{2}\left\{2\times1+\left(20-1\right)\times3\right\}+\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{20.21}\right)$$

$$=\frac{20\times59}{2}$$+

$$\left(\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+.....+\left(\frac{1}{20}-\frac{1}{21}\right)\right)$$

$$=590+\left(1-\frac{1}{21}\right).$$

$$=590+\left(\frac{20}{21}\right).$$

$$=\frac{12410}{21}.$$

A is correct choice.