The sum of the powers 1-2-1-2-2-1-2-3-1-2-4 can be written as-1-1-2-4FalseTrue

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Sum of Powers

The sum of th...

Question

$The sum of the powers$
$\frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}}$
$can be written as = 1 - \frac{1}{2^{4}}$

False

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True

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Similar questions

$\frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} + \frac{1}{2^{5}} + \frac{1}{2^{6}} + \frac{1}{2^{7}}$ =___

1 - \frac{1}{2} + \frac{1}{2} + \frac{1.3}{2.4} . \frac{1}{2^{2}} - \frac{1.3.5}{2.4.6} . \frac{1}{2^{3}} + \frac{1.3.5.7}{2.4.6.8} . \frac{1}{2^{4}} - . . . = \sqrt{\frac{2}{3}}

1 + \frac{1 + 2}{2!} + \frac{1 + 2 + 2^{2}}{3!} + \frac{1 + 2 + 2^{2} + 2^{3}}{4!} \dots . =

\frac{3}{1.2} \cdot \frac{1}{2} + \frac{4}{2.3} \cdot \frac{1}{2^{2}} + \frac{5}{3.4} \cdot \frac{1}{2^{3}} + \frac{6}{4.5} \cdot \frac{1}{2^{4}} + . . . .

1 = \frac{1}{2} (1 \times (1 + 1))

1 + 2 = \frac{1}{2} (2 \times (2 + 1))

1 + 2 + 3 = \frac{1}{2} (3 \times (3 + 1))

1 + 2 + 3 + 4 = \frac{1}{2} (4 \times (4 + 1))

31 + 32 + . . . + 50

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