# How do I find the sum of the series: 4+5+6+8+9+10+12+13+14+⋯+168+169+170. since D is changing from +1, +1 to +2 ?

If we make three sums:

Then :

Finally:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the sum of the series, use the formula for the sum of an arithmetic series: ( S = \frac{n}{2}(a_1 + a_n) ), where ( S ) is the sum, ( n ) is the number of terms, ( a_1 ) is the first term, and ( a_n ) is the last term.

First, find the number of terms: ( n = \frac{a_n - a_1}{D} + 1 )

For this series, ( a_1 = 4 ), ( a_n = 170 ), and ( D ) is changing from ( +1 ) to ( +2 ).

Calculate ( n ) using the formula: ( n = \frac{170 - 4}{1} + 1 = 167 + 1 = 168 )

Now, use the formula for the sum of an arithmetic series: ( S = \frac{168}{2}(4 + 170) = 84 \times 174 = 14616 )

So, the sum of the series is ( 14616 ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #1+1/3+1/9+...+(1/3)^n+...#?
- Integrate the following using infinite #\bb\text(series)# ?
- How do you use the Alternating Series Test?
- What is the Alternating Series Test of convergence?
- Is the sequence divergent or convergent?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7