Question

We can express $(50-1{)}^{49}as(50-1{)}^{49}=5k-1$

• A. True
• B. False

Answer 1

The correct option is A

True

$(50-1{)}^{49}={}^{49}{C}_0(50{)}^{49}-{}^{49}{C}_1(50{)}^{48}+{}^{49}{C}_2(50{)}^{47}............{}^{49}{C}_{48}(50{)}^1-{}^{49}{C}_{49}$

${}^{49}{C}_0(50{)}^{49}-{}^{49}{C}_1(50{)}^{48}+{}^{49}{C}_2(50{)}^{47}............49\times (50{)}^1$ is multiple of 5.We will replace it by 5k.

$(50-1{)}^{49}=5k-1$