Answer:
Option B
Explanation:
Let S10 be the sum of the first ten terms of the series, then we have
$S_{10}= (1\frac{3}{5})^{2}+(2\frac{2}{5})^{2}+(3\frac{1}{5})^{2}+4^{2}+(4\frac{4}{5})^{2}+... to $ 10 terms
$= (\frac{8}{5})^{2}+(\frac{12}{5})^{2}+(\frac{16}{5})^{2}+4^{2}+(\frac{24}{5})^{2}+... to $ 10 terms
= $\frac{1}{5^{2}}({8}^{2}+{12}^{2}+16^{2}+{20}^{2}+{24}^{2}... to $ 10 terms
=$\frac{4^{2}}{5^{2}}({2}^{2}+{3}^{2}+4^{2}+{5}^{2}+... to $ to 10 terms)
= $ \frac{4^{2}}{5^{2}}({2}^{2}+{3}^{2}+4^{2}+{5}^{2}+... +11^{2})$
= $\frac{16}{25}(({1}^{2}+{2}^{2}+3^{2}+{4}^{2}+... +11^{2})-1^{2})$
=$ \frac{16}{25}(\frac{11.(11+1)(2.11+1)}{6}-1)$
=$ \frac{16}{25}(506-1)=\frac{16}{25}\times 505$
$\Rightarrow \frac{16}{5}m=\frac{16}{25}\times 505=101$
