If b is very small as compared to the value of a, so that the cube and other higher powers of b/a can be neglected in the identity 1/(a-b) + 1/(a-2b) + 1/(a-3b) + ... + 1/(a-nb) = αn + βn² + γn³,
If b is very small as compared to the value of a, so that the cube and other higher powers of b/a can be neglected in the identity 1/(a-b) + 1/(a-2b) + 1/(a-3b) + ... + 1/(a-nb) = αn + βn² + γn³,
Option 1 -
(a+b)/3a²
Option 2 -
(a²+b)/3a³
Option 3 -
(b²)/3a³
Option 4 -
(a+b²)/3a³
Asked by Shiksha User
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1 Answer
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Correct Option - 3
Detailed Solution:Σ (1/a) (1-rb/a)? ¹ = (1/a)Σ (1+rb/a+r²b²/a²+.)
≈ (1/a)Σ (1+rb/a) = n/a + (b/a²)n (n+1)/2
Compare coeffs: α=1/a, β=b/2a². γ=b²/3a³. This differs from solution.
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