199-299-399-499-599 is divisible by what numbers-

199+299+399+499+599=199+499+299+399+599We #160;know #160;, #160;xn+an #160;is #160;divisible #160;by #160;x+a #160;. #160;When #160;n #160 ...

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Quantitative Aptitude

Divisibility Rule for 11

199+299+399+4...

Question

1⁹⁹+2⁹⁹+3⁹⁹+4⁹⁹+5⁹⁹ is divisible by what numbers?

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Solution

$1^{99} + 2^{99} + 3^{99} + 4^{99} + 5^{99} = (1^{99} + 4^{99}) + (2^{99} + 3^{99}) + 5^{99} We know, (x^{n} + a^{n}) is divisible by (x + a) . When n is odd . Now, (1^{99} + 4^{99}) is divisible by (1 + 4) = 5 . (2^{99} + 3^{99}) is divisible by (2 + 3) = 5 . 5^{99} is divisible by 5 . So, (1^{99} + 4^{99}) + (2^{99} + 3^{99}) + 5^{99} is also divisible by 5 .$

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Similar questions

Q. What is the remainder when p - q is divided by 100, if

p = 2^{99} + 4^{99} + 6^{99} + 8^{99} + . . . . . . . . . + 100^{99}

and

q = 1^{99} + 3^{99} + 5^{99} + 7^{99} + . . . . . . . . . . + 99^{99} ?

${lim}_{π \to \infty} \frac{1^{99} + 2^{99} + 3^{99} + \dots \dots n^{99}}{n^{100}} =$ [EAMCET 1994]

Q. Draw a histogram of the following frequency distribution table.

Weekly income (Rs.)	200 $-$ 299	300 $-$ 399	400 $-$ 499	500 $-$ 599	600 $-$ 699
24	24	32	78	23	15

Based on the information given in the table, identify the kind of series the table represents :

$\begin{matrix} Marks & Frequency 100 - 199 & 80 200 - 299 & 123 300 - 399 & 34 400 - 499 & 48 \end{matrix}$

$(^{2 n} C_{1})^{2} + 2 \times (^{2 n} C_{2})^{2} + 3. (^{2 n} C_{3})^{2} . . . . . + 2 n (^{2 n} C_{2 n})^{2}$ ,When n = 100

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199+299+399+499+599 is divisible by what numbers?

199+299+399+499+599=199+499+299+399+599We know , xn+an is divisible by x+a . When n is odd.Now,199+499 is divisible by 1+4=5.299+399 is divisible by 2+3=5.599 is divisible by 5.So,199+499+299+399+599 is also divisible by 5.

1⁹⁹+2⁹⁹+3⁹⁹+4⁹⁹+5⁹⁹ is divisible by what numbers?