The number of distinct terms in the expansion of (x+(1/x)+x2+(1/x2))15 is/are (with respect to different power of x)

Question

The number of distinct terms in the expansion of (x+(1/x)+x2+(1/x2))15 is/are (with respect to different power of x) (A) 255 (B) 61 (C) 127 (D) none of these

Tardigrade Admin · Accepted Answer

(x+(1/x)+x2+(1/x2))15=((x3+x+x4+1/x2))15 =(ao+a1x+a2x2+...+a60x60/x30) Hence, the total number of terms is 61.

Q. 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 $x$ )

$255$

$61$

$127$

none of these

$(x + \frac{1}{x} + x^{2} + \frac{1}{x ^{2}})^{15} = (\frac{x ^{3} + x + x ^{4} + 1}{x ^{2}})^{15}$
$= \frac{a _{o} + a _{1} x + a _{2} x ^{2} + ... + a _{60} x ^{60}}{x ^{30}}$
Hence, the total number of terms is 61.

Q. The number of distinct terms in the expansion of (x+x1​+x2+x21​)15 is/are (with respect to different power of x)

255

61

127