Question

B = \(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{64.69}\)

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Answer 1

5B=\(\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+...+\frac{5}{64\cdot69}\)

5B=\(\frac{9-4}{4\cdot9}+\frac{14-9}{9\cdot14}+...+\frac{69-64}{64.69}\)

5B=\(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

5B=\(\frac{65}{276}\)

B=\(\frac{13}{276}\)

Answer 2

\(B=\frac{1}{4.9}+\frac{1}{9.14}+....+\frac{1}{64.69}\)

\(\Rightarrow5B=\frac{5}{4.9}+\frac{5}{9.14}+...+\frac{5}{64.69}\)

\(5B=\frac{9-4}{4.9}+\frac{14-9}{9.14}+....+\frac{69-64}{64.69}\)

\(5B=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\)

\(5B=\frac{1}{4}-\frac{1}{69}\)

\(5B=\frac{65}{276}\)

\(B=\frac{65}{276}:5\)

\(B=\frac{13}{276}\)

Answer 3

\(B=\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{64.69}\)

\(5B=\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{64.69}\)

\(5B=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}+...+\frac{1}{64}-\frac{1}{69}\)

\(5B=\frac{1}{4}-\frac{1}{69}\)

\(5B=\frac{65}{276}\)

\(B=\frac{65}{276}:5\)

\(B=\frac{13}{276}\)

Answer 4

\(B=\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+.....+\frac{1}{64\cdot69}\)

\(5B=\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+\frac{5}{14\cdot19}+....+\frac{5}{64\cdot69}\)

\(5B=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+....+\frac{1}{64}-\frac{1}{69}\)

\(5B=\frac{1}{4}-\frac{1}{69}\)

\(B=\frac{\frac{1}{4}-\frac{1}{69}}{5}\)