Binomial Theorem And Its Simple Applications Question 137
Question: The number of distinct terms in the expansion of $ {{( x+\frac{1}{x}+x^{2}+\frac{1}{x^{2}} )}^{15}} $ is/are (with respect to different power of x)
Options:
A) 255
B) 61
C) 127
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ {{( x+\frac{1}{x}+x^{2}+\frac{1}{x^{2}} )}^{15}}={{( \frac{x^{3}+x+x^{4}+1}{x^{2}} )}^{15}} $
$ =\frac{a_0+a_1x+a_2x^{2}+…+a_{60}x^{60}}{x^{30}} $
Hence, the total number of terms is 61.
BETA
