Mathematics, 28.05.2021 14:00, silvajimena74
if {a \index{n}} be an Arithmetic sequence , calculate \frac{1}{a1a2} + \frac{1}{a2a3} +...+ \frac{1}{a39a40}ā
Answers: 1
is an arithmetic sequence.
.![=\dfrac{d}{d}\left[\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\right]](/tpl/images/1353/3057/45984.png)
![=\dfrac{1}{d}\left[\dfrac{d}{a_1a_2}+\dfrac{d}{a_2a_3}+...+\dfrac{d}{a_{39}a_{40}}\right]](/tpl/images/1353/3057/8c2e8.png)
![=\dfrac{1}{d}\left[\dfrac{a_2-a_1}{a_1a_2}+\dfrac{a_3-a_2}{a_2a_3}+...+\dfrac{a_{40}-a_{39}}{a_{39}a_{40}}\right]](/tpl/images/1353/3057/6af63.png)
![=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_2}+\dfrac{1}{a_2}-\dfrac{1}{a_3}+....+\dfrac{1}{a_{39}}-\dfrac{1}{a_{40}}\right]](/tpl/images/1353/3057/46688.png)
![=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_{40}}\right]](/tpl/images/1353/3057/0303e.png)
![=\dfrac{1}{d}\left[\dfrac{a_{40}-a_1}{a_1a_{40}}\right]](/tpl/images/1353/3057/f46da.png)
![=\dfrac{1}{d}\left[\dfrac{a_1+(40-1)d-a_1}{a_1a_{40}}\right]](/tpl/images/1353/3057/57e1a.png)
Ā Ā Ā ![[\because a_n=a_1+(n-1)d]](/tpl/images/1353/3057/d7df5.png)
![=\dfrac{1}{d}\left[\dfrac{39d}{a_1a_{40}}\right]](/tpl/images/1353/3057/dc59e.png)
.
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if {a \index{n}} be an Arithmetic sequence , calculate \frac{1}{a1a2} + \frac{1}{a2a3} +...+ \frac{1...
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