Find the numerical answer to the summation given below. sum_(n=0)^(95)(5n+7) Answer:

Separate Summation Parts: To find the sum of the series, we can separate the summation into two parts: the summation of 5n from n=0 to n=95 and the summation of 7 from n=0 to n=95.Find Sum of 5n Series: First, let's find the sum of the arithmetic series 5n. The sum of an arithmetic series is given by the formula S = (n/2)(a_1 + a_n), where n is the number of terms, a_1 is the first term, and a_n is the last term.Calculate Sum of 5n: The first term a_1 when n=0 is 5(0) = 0, and the last term a_n when n=95 is 5(95) = 475. The number of terms is 95 - 0 + 1 = 96.Calculate Sum of 7: Now we can calculate the sum of the arithmetic series 5n: S = (96/2)(0 + 475) = 48 * 475.Add Two Sums: Calculating the sum gives us S = 48 * 475 = 22800.Find Total Sum: Next, we calculate the sum of the constant 7 added 96 times (from n=0 to n=95). This is simply 7 multiplied by the number of terms, which is 96.Calculating this sum gives us 7 * 96 = 672.Finally, we add the two sums together to find the total sum of the series: 22800 (sum of 5n) + 672 (sum of 7).Adding these together gives us the final sum: 22800 + 672 = 23472.

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Find the numerical answer to the summation given below.

sum_(n=0)^(95)(5n+7)
Answer:

Find the numerical answer to the summation given below. $\newline$ $\sum_{n=0}^{95}(5 n+7)$ $\newline$ Answer:

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Q. Find the numerical answer to the summation given below.

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\sum_{n=0}^{95}(5 n+7)

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Answer:

Separate Summation Parts: To find the sum of the series, we can separate the summation into two parts: the summation of $5n$ from $n=0$ to $n=95$ and the summation of $7$ from $n=0$ to $n=95$ .
Find Sum of $5$ n Series: First, let's find the sum of the arithmetic series $5n$ . The sum of an arithmetic series is given by the formula $S = \frac{n}{2}(a_1 + a_n)$ , where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term.
Calculate Sum of $5n$ : The first term $a_1$ when $n=0$ is $5(0) = 0$ , and the last term $a_n$ when $n=95$ is $5(95) = 475$ . The number of terms is $95 - 0 + 1 = 96$ .
Calculate Sum of $7$ : Now we can calculate the sum of the arithmetic series $5n$ : $S = (\frac{96}{2})(0 + 475) = 48 \times 475$ .
Add Two Sums: Calculating the sum gives us $S = 48 \times 475 = 22800$ .
Find Total Sum: Next, we calculate the sum of the constant $7$ added $96$ times (from $n=0$ to $n=95$ ). This is simply $7$ multiplied by the number of terms, which is $96$ .
Find Total Sum: Next, we calculate the sum of the constant $7$ added $96$ times (from $n=0$ to $n=95$ ). This is simply $7$ multiplied by the number of terms, which is $96$ .Calculating this sum gives us $7 \times 96 = 672$ .
Find Total Sum: Next, we calculate the sum of the constant $7$ added $96$ times (from $n=0$ to $n=95$ ). This is simply $7$ multiplied by the number of terms, which is $96$ .Calculating this sum gives us $7 \times 96 = 672$ .Finally, we add the two sums together to find the total sum of the series: $22800$ (sum of $5n$ ) + $672$ (sum of $7$ ).
Find Total Sum: Next, we calculate the sum of the constant $7$ added $96$ times (from $n=0$ to $n=95$ ). This is simply $7$ multiplied by the number of terms, which is $96$ .Calculating this sum gives us $7 \times 96 = 672$ .Finally, we add the two sums together to find the total sum of the series: $22800$ (sum of $5n$ ) + $672$ (sum of $7$ ).Adding these together gives us the final sum: $96$ $1$ .