Question

(-1)+(-1)+(-1)+(-1)+........500 times=

Answer 1

Answer:

The required answer is $-500$.

Step-by-step explanation:

The nth term in a series: $A _{n}= a + (n - 1)d$ is the formula for the nth term of an arithmetic series. The common difference, or $d$, is the difference between any two consecutive terms in an arithmetic series; it can be calculated by deducting any pair of terms starting with $a$ and $an+1$.

Given: the series is $(-1)+(-1)+(-1)+(-1)+........500 times$

To find: the value of the given series.

Solution:

Here,

Take(-1) common in that series.

$(-1)+(-1)+(-1)+(-1)+........500 times=-(1+1+1+1+........500 times)$

$=(-500)$

Therefore, the answer is $-500$.

#SPJ3

Answer 2

The sum of the given series is -500.

Given,

A series (-1)+(-1)+(-1)+(-1)+........500 times.

To Find,

The sum of this series.

Solution,

The given series is

(-1)+(-1)+(-1)+(-1)+........500 times

The given series is an A.P where

a = first term of A.P = -1

d = common difference = -1+1 = 0

n = number of terms = 500

Now, the formula of sum of terms of an A.P is

S = n/2(a+an)

substituting the values

S = 500/2(-1-1)

S = -500

Hence, the sum of the given series is -500.

#SPJ1