Q. 685.0( 1 Vote )

# Find the sum of the following series upto n terms Tn = = = Let = ……(i)

⇒ 1 = A(n + 1) + Bn ……(ii)

[On multiplying both sides by n(n+1)]

To find A : Putting n = 0 in (ii), we get,

1 = A(0 + 1) ⇒ A = 1

To find B : Putting n = 0 in (ii), we get

1 = B(-1) ⇒ B = -1

Putting these values of A and B in (i), the partial fractions are = or Tn = Putting n = 1, 2, 3,……n, we get,

T1 = T2 = T3 = ………………….

Tn = Sn = 1 - = Extra. Hence find sum to infinity:

Now, Sn = = As n → ∞ or S∞ = = 0

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