×

Limit Problem

$$\displaystyle \lim_{x\to\frac{\pi}{2}} \frac{(1+\tan x)^{10}+(2+\tan x)^{10}+(3+\tan x)^{10}.....(20+\tan x)^{10}}{\tan^{9}x}-20\tan x=?$$

Note by Krishna Jha
3 years, 10 months ago

Sort by:

Taking the LCM and then considering the expansion of all the terms

Now first 9 terms of expansion will result a polynomial in tanx of degree 8 or lower.

Hence it would tend to zero as x»π/2 Hence writing the last two terms of the expansion

We would get the limit basically as the coefficient of (tan⁡x)^9 in the numerator as =10C9[1+2+3+ …. 20] = 10[20*21/2] = 2100 · 3 years, 10 months ago

Thanks... It didnt strike me... · 3 years, 10 months ago

Where did you get such horrible problem from? · 3 years, 10 months ago

"Horrible" in what sense???? Btw i got it in a test..could'nt solve it.. · 3 years, 10 months ago

No way this problem is horrible. · 3 years, 10 months ago

You mean easy?? · 3 years, 10 months ago