Question

Question 4 Find the sum to n terms of the series 1/1x2 + 1/2x3 + 1/3x4 + ...

Class X1 - Maths -Sequences and Series Page 196

Answer 1

Let S = 1/(1 × 2) + 1/(2 × 3) + 1/(3 × 4) + .........
Here, we can observed that ,
Tn = 1/(nth term of 1,2,3....)(nth term of 2,3,4...)
= 1/{1+(n-1)×1}{2+(n-1)×1}
=1/n(n+1)
= 1/n - 1/(n+1)
now, putting n = 1, 2, 3, 4, ........
T1 = 1/1 - 1/(1+1) = 1/1 - 1/2
T2 = 1/2 - 1/(2+1) = 1/2 - 1/3
T3 = 1/3 - 1/(3+1) = 1/3 - 1/4
................
................
Tn = 1/n - 1/(n+1)
now, add all terms , then we get
S = T1 + T2 + T3 + ........+ Tn
= (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) +......(1/n - 1/(n+1) )
= 1 - 1/(n+1)
= n/(n+1)

Answer 2

Answer:

Step-by-step explanation:

tn=1/n(n+1)

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

substitute 1 in vn-1 and n in vn

tn=1-(1/n+1)

tn=n/n+1