If (a\_n=\frac{-2}{4 n^2-16 n+15}), then (a\_1+a\_2+\ldots \... | Mathematics | SolveeIt

If $a_n=\frac{-2}{4 n^2-16 n+15}$ , then $a_1+a_2+\ldots \ldots+a_{25}$ is equal to:

$\frac{52}{147}$

$\frac{50}{141}$

$\frac{51}{144}$

$\frac{49}{138}$

Answer

$\frac{50}{141}$

Explanation

If an=4n2−16n+15−2 then a1+a2+………a25
⇒n=1∑25an=∑4n2−16n+15−2
=∑4n2−6n−10n+15−2
=∑2n(2n−3)−5(2n−3)−2
=∑(2n−3)(2n−5)−2
=∑2n−31−2n−51
=471−(−3)1
=14150

Mathematics Question on Differential equations