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Find the numerically greatest term in th...

Find the numerically greatest term in the expansion of `(2x+5 y)^(34)w h e n x=3 and y=2.`

Text Solution

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We have `(3-5x)^(15)`
For `|(T_(r+1))/(T_(r))|=(15-r+1)/(r) |-(5x)/(3)|ge 1`
`rArr (16-r)/(r).(5xx1/5)/(3)ge1 " "("Putting" x = 1//5)`
`rArr 16 - r ge 3r`
`rArr le 4`
Hence, `T_(4)` and `T_(5)` numerically the greatest terms,
`T_(4) = .^(15)C_(3)3^(15-3)(-5x)^(3)`
`= (-455 xx 3^(12) xx 5^(3))x^(3)`
and `T_(5) = .^(15)C_(4)3^(15-4)(-5x)^(4)`
`= (455 xx 3^(12) xx 5^(3))x^(4)`
Also , for numerical value,
`|T_(4)| = |T_(5)| = 455 xx 3^(12) 5^(3)`
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