Đáp án:
Giải thích các bước giải:
\(\frac{2^2}{1.3}+\frac{3^2}{2.4}+\frac{4^2}{3.5}+....+\frac{50^2}{49.51}\)
\(=\frac{2^2-1}{1.3}+\frac{3^2-1}{2.4}+....+\frac{50^2-1}{49.51}+\frac{1}{1.3}+\frac{1}{2.4}+....+\frac{1}{49.51}\)
\(=\left(1+1+....+1\right)+\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{2}-\frac{1}{4}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{51}\right)\)(49 chữ số 1)
\(=49+\frac{1}{2}.\left[\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{49}\right)-\left(\frac{1}{3}+\frac{1}{4}+...+\frac{1}{51}\right)\right]\)
\(=49+\left(\frac{3}{2}-\frac{1}{50}-\frac{1}{51}\right):2\)
\(=49 + \frac{1862}{1275} : 2 \)
\(=49+\frac{931}{1275}\)
\( =49 \frac{931}{1275} \)
ngắn gọn
\(A =\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{50^2}{49.51}\)
$ = \frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}......\frac{50.50}{49.51}$
$= \frac{2.2.3.3.4.4...99.99}{1.2.3.4....100.3.4...98}$
$= \frac{2.99}{100}$
$= \frac{99}{50} $
Chúc bạn học tốt !!!
