Dear Student,Solution) x-1x10Now, Tr+1=Crnxn-r-1xr to get the constant term n-r=rn=2r10=2rr=10/2r=5So,T5+1=C510x10-5 -1x5T6=C510x5 x-5-15=-C510x5+(-5)=-C510x0=-C510T6=-C510=-10×9×8×7×6×5!5!×5×4×3×2×1=-252Regards!

Find Constant term

D e a r S t u d e n t, S o l u t i o n) {(x - \frac{1}{x})}^{10} N o w, T_{r + 1} = {}^{n}C_{r} x^{n - r} {(\frac{- 1}{x})}^{r} t o g e t t h e c o n s \tan t t e r m . n - r = r n = 2 r 10 = 2 r r = 10 / 2 r = 5 S o, T_{5 + 1} = {}^{10}C_{5} x^{10 - 5} {(\frac{- 1}{x})}^{5} T_{6} = {}^{10}C_{5} x^{5} x^{- 5} {(- 1)}^{5} = - {}^{10}C_{5} x^{5 + (- 5)} = - {}^{10}C_{5} x^{0} = - {}^{10}C_{5} T_{6} = - {}^{10}C_{5} = \frac{- 10 \times 9 \times 8 \times 7 \times 6 \times 5!}{5! \times 5 \times 4 \times 3 \times 2 \times 1} = - 252 R e g a r d s!

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