Question

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

Answer 1

Answer:

(a) 498501

(b) 251001

Step-by-step explanation:

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

$sum=\frac{n(a_1+a_n)}{2}$         .... (1)

where, n is number of terms.

(a)

The given series is

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

here,

$a_1=1$

$a_n=998$

$n=998$

Substitute $a_1=1$, $a_n=998$ and $n=998$ in equation (1).

$sum=\frac{998(1+998)}{2}$

$sum=499(999)$

$sum=498501$

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.

$a_1=1$

$a_n=1001$

$n=501$

Substitute $a_1=1$, $a_n=1001$ and $n=501$ in equation (1).

$sum=\frac{501(1+1001)}{2}$

$sum=\frac{501(1002)}{2}$

$sum=501(501)$

$sum=251001$

Therefore the sum of series is 251001.