Test Index

Sequence and Series

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Question : 26 of 86

Marks: +1, -0

The sum of the series

1-1+1-1+1-1+. . . . . .

to 100 terms is equal to

1
-1
0
50

Solution:

Concept:

The series alternates between

1

and

-1

, and there are an even number of terms.

Explanation:

The series is

1-1+1-1+1-1+\ldots

to 100 terms.

Group terms in pairs:

(1-1)+(1-1)+\ldots

There are 50 such pairs (since 100 terms ÷ 2 = 50).

Each pair sums to

0

.

Therefore, total sum

= 50 \times 0 = 0

.

Answer:

0

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