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The larger of 99^{50}+100^{50} is 101^{50} is ________.

Question

The larger of $9 9^{50} + 10 0^{50}$ is $10 1^{50}$ is ________.

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The larger of

9 9^{50} + 10 0^{50}

10 1^{50}

is ________.

15 mins ago

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Text solutionVerified

We have,

10 1^{50} = (100 + 1)^{50} = 10 0^{50} + 50 \times 10 0^{49} + \frac{50 \times 49}{2 \times 1} 10 0^{48} + ... (1)

9 9^{50} = (100 - 1)^{50} = 10 0^{50} - 20 \times 10 0^{49} + \frac{50 \times 49}{2 \times 1} 10 0^{48} - ...

Subtracting (2) from (1), we get

10 1^{50} - 9 9^{50} = 10 0^{50} + 2 \frac{50 \times 49 \times 48}{1 \times 2 \times 3} 10 0^{47} + ... > 10 0^{50}

Hence,

10 1^{50} > 10 0^{50} + 9 9^{50}

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