Question

1+3+5+7+9...997+999= решите пжалисту

Answer 1

Это ничто иное как арифметическая прогрессия с первым членом $a_1=1$ и разностью $d=2$

$S_n= \dfrac{2a_1+(n-1)d}{2}\cdot n$ - сумма первых n членов арифметической прогрессии

Для меня трудно определить сколько всего n членов в этой прогрессии. Но это не беда! Согласно формуле n-го члена арифметической прогрессии имеем, что 
   $a_n=a_1+(n-1)d;~~~~~~~999=1+2(n-1)$

$998=2n-2\\ 1000=2n\\ n=500$

То есть, нам нужно найти сумму первых 500 членов арифметической прогрессии.
  $S_{500}= \dfrac{2a_1+499d}{2} \cdot 500= \dfrac{2\cdot 1+499\cdot 2}{2} \cdot 500=250000$- ответ

Второй способ.

1+3+5+...+995+997+999 = (1+999) + (3+997) + (5+995) + .+(499+501) = 
=1000*250 = 250000 

Answer 2

To find the sum of the series 1 + 3 + 5 + 7 + 9 + ... + 997 + 999, we can use the formula for the sum of an arithmetic series.

Formula for the sum of an arithmetic series:

The sum of an arithmetic series can be calculated using the formula:

S = (n/2)(a + l)

Where: - S is the sum of the series - n is the number of terms in the series - a is the first term of the series - l is the last term of the series

In this case, the first term (a) is 1, the last term (l) is 999, and the common difference between terms is 2.

Calculating the number of terms:

To find the number of terms (n) in the series, we can use the formula:

n = (l - a)/d + 1

Where: - n is the number of terms - l is the last term - a is the first term - d is the common difference

In this case, the last term (l) is 999, the first term (a) is 1, and the common difference (d) is 2.

Using the formula, we can calculate the number of terms:

n = (999 - 1)/2 + 1 = 499

Calculating the sum:

Now that we know the number of terms (n), we can calculate the sum (S) using the formula for the sum of an arithmetic series:

S = (n/2)(a + l)

Substituting the values:

S = (499/2)(1 + 999) = 249500

Therefore, the sum of the series 1 + 3 + 5 + 7 + 9 + ... + 997 + 999 is 249500.

Please note that this calculation assumes that the series is an arithmetic series with a common difference of 2.