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Find the sum: 1-1/8+1/8xx3/(16)-(1xx3xx5...

Find the sum: `1-1/8+1/8xx3/(16)-(1xx3xx5)/(8xx16xx24)+...`

Text Solution

Verified by Experts

Comparing the given series to
`1+nx + (n(n-1))/(2!) x^(2) + "…." = (1+x)^(n)`
we get
` nx = -1/8` and `(n(n-1))/(2!) x^(2) = 3/128`
or `x = 1/4, n = - 1/2`
Hence,
`1-1/(8)+(1)/(8)(3)/(16)-"…."=(1+(1)/(4))^(-1//2) = (2)/(sqrt(5))`
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