Question

Find the value of the series : (1/(1x3x5)) + (1/(3x5x7)) + (1/(5x7x9)) + ..... upto 10 terms.
O 60/483
30/483
40/483
50/483​

Answer 1

Answer:

183/483

Step-by-step explanation:

let

1/n(n+1)(n+2) = a/n + b/n+1 + c/n+2  , partial fractions

1 = a(n+1)(n+2) + bn(n+2) + cn(n+1)

@ n = 0 , a = 1/2

@ n = -1 , b = -1

@ n = -2 , c = 1/2

2/n(n+1)(n+2) = 1/n -2/n+1 + 1/n+2

(2/(1x3x5)) + (2/(3x5x7)) + (2/(5x7x9)) + ..... upto 10 terms

= 1-2/3 +1/5 +1/3-2/5 + 1/7 + 1/5 -2/7 +1/9 +1/7 -2/9 + 1/11 ..... + 1/19 - 2/21 + 1/23

= 1-1/3 - 1/21 + 1/23 = 2/3 + 44/21x23

therefore

(1/(1x3x5)) + (1/(3x5x7)) + (1/(5x7x9)) + ..... upto 10 terms.

= 1/3 + 22/21x23 = 183/483