1. (10 points) Calculate: $\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+\frac{9}{400}+\frac{11}{900}+\frac{13}{1764}+\frac{15}{3136}=$
【Analysis】By observation, each fraction can be decomposed into the form of the difference of two fractions, and then the result can be obtained through addition and subtraction cancellation.

【Solution】Solution: $\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+\frac{9}{400}+\frac{11}{900}+\frac{13}{1764}+\frac{15}{3136}$
$$
\begin{array}{l}
=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{25}+\frac{1}{25}-\frac{1}{36}+\frac{1}{36}-\frac{1}{49}+\frac{1}{49}-\frac{1}{64} \\
=1-\frac{1}{64} \\
=\frac{63}{64} .
\end{array}
$$

Therefore, the answer is: $\frac{63}{64}$.