First slide

Binomial theorem for positive integral Index

Question

The number of terms in the expansion of $(2 x + 3 y - 4 z)^{n},$ is

Moderate

A

$n + 1$
B

$n + 3$
C

$\frac{(n + 1) (n + 2)}{2}$
D

none of these

Solution

Total number of terms in the expansion of
$(2 x + 3 y - 4 z)^{n},$ is
$^{n + 3 - 1} C_{3 - 1} =^{n + 2} C_{2} = \frac{(n + 2) (n + 1)}{2}$

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