Question

in 1-2+3-4+5-6+.... series find s41 in ap​

Answer 1

SOLUTION

GIVEN

$\sf{1 - 2 + 3 - 4 + 5 - 6 + .. ..}$

TO DETERMINE

$\sf{S_{41} \: \:in \: \: AP}$

EVALUATION

Here the series is

$\sf{1 - 2 + 3 - 4 + 5 - 6 + .. ..}$

Which is of the form

$\sf{ {( - 1)}^{n + 1} \: n \: \: \: where \: \: n \in \mathbb{N} }$

Hence

$\sf{1 - 2 + 3 - 4 + 5 - 6 + .. ..}$

$\sf{ = 1 - 2 + 3 - 4 + 5 - 6 + .. + 41}$

$\sf{ =( 1 - 2) +( 3 - 4 )+ (5 - 6 )+ .. +(39 - 40) + 41}$

There are 20 brackets

$\sf{ = - 1 - 1 - 1 \: .... - 1 + 41}$

The number of - 1 is 20

$= - 20 + 41$

$= 21$

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