If a_n=-2 4 n^2-16 n+15 , then a_1+a_2+ +a_ 25 is equal to : - Vidyadip

MCQ

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

A
$\frac{51}{144}$
B
$\frac{49}{138}$
✓
$\frac{50}{141}$
D
$\frac{52}{147}$

✓

Answer

Correct option: C.

$\frac{50}{141}$

c
If $a_n=\frac{-2}{4 n^2-16 n+15}$ then $a_1+a_2+\ldots \ldots \ldots a_{25}$

$\sum \limits_{n=1}^{25} a_n=\sum \frac{-2}{4 n^2-16 n+15}$

$=\sum \frac{-2}{4 n^2-6 n-10 n+15}$

$=\sum \frac{-2}{2 n(2 n-3)-5(2 n-3)}$

$=\sum \frac{-2}{(2 n-3)(2 n-5)}$

$=\sum \frac{1}{2 n-3}-\frac{1}{2 n-5}$

$=\frac{1}{47}-\frac{1}{(-3)}$

$=\frac{50}{141}$

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