Question

can someone help me with evaluating a finite series for the specified number of terms?

Answer 1

hey I can help u

Answer 2

the question is 13+15+17+19+... ; n=11

Answer 3

like how do you do it?

Answer 4

whp can help me please???

Answer 5

Hi. Is this an arithmetic or geometric series?

Answer 6

We need to know which form it is so we can use the appropriate formula for the sum.

If it is an arithmetic series, we can write the equation for an individual term as

\[a_n = a_1 + (n-1)d\]where \(n\) is the number of the term of interest,
\(a_n\) is the value of the term of interest
\(d\) is the common difference

The sum for \(n\) terms is then given by
\[S_n = \frac{n}{2}(a_1 + a_n) = \frac{n}{2}(a_1 + (a_1+(n-1)d)) = \frac{n}{2}(2a_1 + (n-1)d)\]

Answer 7

You can think of this turning the series into pairs of numbers which all have the same sum:

for example, adding up 1-6 could be done as
1+2+3+4+5+6 or
(1+6) + (2+5) + (3+4) = 7+7+7 = 3*7 = 21

This formula takes the first and last numbers in the series, adds them, then multiplies by half the number of such pairs we have. As it turns out, if there is an odd number of terms, the "leftover" number is the one in the middle, and the right thing happens.

1-7:
(1+7) + (2+6) + (3+5) + 4
3 pairs adding to 8, one lone number which is half of 8

8+8+8+4 = 3*8 + 4 = 3*8 + 0.5*8 = 3.5*8 = 28

checking our work the long way,
1+2+3+4+5+6+7 = 3+3+4+5+6+7 = 10+5+6+7 = 15 + 6 +7 = 15+13=28

the formula is easier, especially if we have many terms. There's a famous anecdote about a mathematician named Gauss who as a child was assigned the problem of summing the numbers from 1 to 100. His classmates all worked hard, but none got the right answer. Gauss thought for a moment and immediately wrote down the correct answer, demonstrating that sometimes it's better to think a bit about the problem instead of just diving into the calculations.