To find : coefficients of x7 and x8
Formula : tr+1 = (rn)an-rbr
Here, a=2, b = \(\frac{x}{3}\)
We have, tr+1 = (rn)an-rbr
tr+1 = (rn)(2)n-r\(\Big(\frac{x}{3}\Big)\) r
= (rn) \(\frac{2^{n-r}}{3^r}\) xr
To get a coefficient of x7 , we must have,
x7 = xr
• r = 7
Therefore, the coefficient of x7 = = (rn) \(\frac{2^{n-7}}{3^7}\)
And to get the coefficient of x8 we must have,
x8 = xr
• r = 8
Therefore, the coefficient of x8 = (8n) \(\frac{2^{n-8}}{3^8}\)
Conclusion :
• Coefficient of x7 = (7n) \(\frac{2^{n-7}}{3^7}\)
• Coefficient of x8 = (8n) \(\frac{2^{n-8}}{3^8}\)