The sum of the coefficients of the first three terms in the expansion of (x-3/x2)m , x is not equal to 0,m being a natural number, is 559. Find the term of the wxpansion containing x3 . (NCERT PG 174 EXAMPLE NO 16). The steps in the NCERTbook are not clear..

The coefficients of the first three terms of are mC0, (–3) mC1and (-3)2 mC2

Therefore, by the given condition, we have
mC0 –3 mC1+ 9 mC2 = 559

since m is a natural number

m = 12

Now, Tr + 1 = 12Cr x12 – r = = 12Cr (– 3)r . x12 – 3r

Since we need the term containing x3

⇒ 12 - 3r = 3

⇒ 3r = 12 - 3 = 9

r = 3

Hence, the required term is 12C3 (– 3)3 x3 = =  – 5940 x3.

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