Question

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{9.10}\)

Answer 1

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(=\frac{1}{2}-\frac{1}{10}\)

\(=\frac{4}{10}\)

\(=\frac{2}{5}\)

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Answer 2

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{9.10}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{10}\)

\(=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)

Answer 3

1/2.3 + 1/3.4 + 1/4.5 + ... + 1/9.10

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10

= 1/2 - 1/10

= 5/10 - 1/10

= 4/10 = 2/5

Answer 4

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10

=1/2-1/10

=2/5 

Answer 5

=1/2 - 1/3+ 1/3-1/4+1/4-1/5+1/5-1/6....+1/9-1/10

= 1/2-1/10

Answer 6

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)

=\(\frac{1}{2}-\frac{1}{10}\)

=\(\frac{2}{5}\)

Answer 7

1/2.3 + 1/3.4 + 1/4.5 + ... + 1/9.10

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +...+ 1/9 - 1/10

= 1/2 - 1/10

= 5/10 - 1/10

= 4/10

= 2/5.