If an=(-2/4 n2-16 n+15), then a1+a2+ ldots ldots+a25 is equal to:

Question

If an=(-2/4 n2-16 n+15), then a1+a2+ ldots ldots+a25 is equal to: (A) (52/147) (B) (50/141) (C) (51/144) (D) (49/138)

Tardigrade Admin · Accepted Answer

If an=(-2/4 n2-16 n+15) then a1+a2+ ldots ldots ldots a25 ⇒ displaystyle∑n=125 a n =∑ (-2/4 n 2-16 n +15) =∑ (-2/4 n2-6 n-10 n +15) =∑ (-2/2 n (2 n -3)-5(2 n -3)) =∑ (-2/(2 n-3)(2 n-5)) =∑ (1/2 n-3)-(1/2 n-5) =(1/47)-(1/(-3)) =(50/141)

Q. If $a_{n} = \frac{- 2}{4 n ^{2} - 16 n + 15}$ , then $a_{1} + a_{2} + \dots\dots + a_{25}$ is equal to:

$\frac{52}{147}$

$\frac{50}{141}$

$\frac{51}{144}$

$\frac{49}{138}$

Q. If an​=4n2−16n+15−2​, then a1​+a2​+……+a25​ is equal to:

14752​

14150​

14451​

13849​

If an​=4n2−16n+15−2​ then a1​+a2​+………a25​ ⇒n=1∑25​an​=∑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​

Q. If $a_{n} = \frac{- 2}{4 n ^{2} - 16 n + 15}$ , then $a_{1} + a_{2} + \dots\dots + a_{25}$ is equal to:

$\frac{52}{147}$

$\frac{50}{141}$

$\frac{51}{144}$

$\frac{49}{138}$