Q 1 The value of ∑r=010 Cr10 3r -210-r is - Maths - Binomial Theorem

Question

Q 1 The value of ∑ r = 0 10 · C r 10 · 3 r
· - 2 10 - r is

Shruti Tyagi · Accepted Answer

Dear Student,

using binomial expansion we knowa-bn=∑r=0nCrn×an-k×-bkcomparing this to the given problem we get∑r=010Cr10×-210-r×3rhence we gwta=-2 and -b=3⇒a=-2 and b=-3we get∑r=010Cr10×-210-r×3r=-2--310=3-210=110=1Hence value of ∑r=010Cr10×-210-r×3r=1
Regards,

Q.1. The value of ∑ r = 0 10 · C r 10 · 3 r · - 2 10 - r is

Q.1. The value of $\sum_{r = 0}^{10} \cdot {}^{10}C_{r} \cdot 3^{r} \cdot {(- 2)}^{10 - r}$ is