R2D2

Algebra Level 3

∑ r = 1 15 r ⋅ 2 r ( r + 2 ) ! = ? \large \displaystyle\sum_{r=1}^{15} \frac{r \cdot 2^{r}}{(r+2)!} = \ ?

16 ! − 2 15 16 ! \frac{16!-2^{15}}{16!} 15 ! − 2 14 15 ! \frac{15!-2^{14}}{15!} 17 ! − 2 16 17 ! \frac{17!-2^{16}}{17!} 18 ! − 2 17 18 ! \frac{18!-2^{17}}{18!}

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Aditya Lalbondre by Aditya Lalbondre , 22, India

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1 solution

Karan Shekhawat
Apr 25, 2015

SimplestTelescopic...

Hint : r = ( r + 2 ) − ( 2 ) r=(r+2)-(2)

Now do yourself , so that You understand it better !

1 Helpful 0 Interesting 0 Brilliant 1 Confused

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Right. Can you elaborate more on it?

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