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Rufina [12.5K]
3 years ago
5

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 i

s
Mathematics
1 answer:
valkas [14]3 years ago
8 0

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.

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