Use gauss's approach to find the following sums (do not use formulas) a 1+2+3+4 998 b. 1+3+5 7+ 1001 a the sum of the sequence is

(a) 498501

(b) 251001

Step-by-step explanation:

According Gauss's approach, the sum of a series is

        .... (1)

where, n is number of terms.

(a)

The given series is

1+2+3+4+...+998

here,

Substitute , and in equation (1).

Therefore the sum of series is 498501.

(b)

The given series is

1+3+5+7+...+ 1001

The given series is the sum of dd natural numbers.

In 1001 natural numbers 500 are even numbers and 501 are odd number because alternative numbers are even.

Substitute , and in equation (1).

Therefore the sum of series is 251001.

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: