Question

State true or false:

${99}^{50}+{100}^{50}$ is greater than ${101}^{50}$

• A. True
• B. False

Answer 1

The correct option is B False

Let's try to find out ${101}^{50}-{99}^{50}$ in terms of remaining term i.e.

${101}^{50}-{99}^{50}=(100+1{)}^{50}-(100-1{)}^{50}$

$=(C_0{.100}^{50}+C_1{.100}^{49}+C_2{.100}^{48}+......)$
$=(C_0{.100}^{50}-C_1{.100}^{49}+C_2{.100}^{48}-......)$
$=2[C_1{.100}^{49}+C_3{.100}^{47}+.........]$
$=2[{50.100}^{49}+C_3{.100}^{47}+.........]$
$={100}^{50}+2[C_3{.100}^{47}+............]$$>{100}^{50}$
$\Rightarrow {101}^{50}>{99}^{50}+{100}^{50}$