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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

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Answer:

(a) 498501

(b) 251001

Explanation:

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


sum=(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=(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=(501(1+1001))/(2)


sum=(501(1002))/(2)


sum=501(501)


sum=251001

Therefore the sum of series is 251001.

User AGM Tazim
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