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If S = 1 - 2² + 3² - 4² upto n terms and n is even, then find S.

2 Answers

337

Sayan Sinha ·2013-07-15 12:16:25

S= 1 + (- 4 + 9) + (- 16 + 25) + (- 36 + 49) ... n
â†’ S= 1 + 5 + 9 + 13 ... n
a₁= 1.
d=4.

So, ans= (2*a₁ + (n-1) d) n2
= (2n-1) n.

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Sayantan Hazra Simple check : Put n = 2...... :)
Upvote·0· Reply ·2013-07-15 12:43:45
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337

Sayan Sinha ·2013-07-19 10:21:34

S= a₁ - a₂ + ... a_n
â†’ S= a₁ + (-a₂ + a₃)... +(-a_n-2+ a_n-1) +a_n.

Our series is (-a₂ + a₃)... +(-a_n-2+ a_n-1)

This series has (n-2)/2 terms.
So, formula gives answer, (2*5 + (((n-2)/2)-1 )* 4)n-24

= (7-n) (n-2)2

Now, we have to add the first and last terms.
So final answer = 1 + (7-n) (n-2)2 + nth term...

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Sayantan Hazra Check : Put n = 4 ........ :)
Upvote·0· Reply ·2013-07-19 11:13:40
Sayan Sinha This one works when n is odd.
Upvote·0· Reply ·2013-07-19 23:53:59
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