Test:1 QNo:3

BITSAT Sample Questions › Disucss Test Questions questions › Test:1 QNo:3

Evaluate: 1² -2² +3² -4² + ...... +99² -100²

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6 Answers

1

abhinavgiri giri ·2009-09-26 09:32:33

i dont get it bro...cud u pls. help

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3

msp ·2009-09-26 09:48:21

club the terms like

1²-2²=(1+2)(1-2)

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1

Bicchuram Aveek ·2009-09-26 13:07:33

1²-2² = -3
3²-4² = -7
5²-6² = -11

So u get an AP of 50 terms :-)

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62

Lokesh Verma ·2009-09-26 23:28:34

The given expression is equal to

-(1+2+3+4+....100) :)

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1

varun.tinkle ·2009-10-17 18:56:43

or u can use summation series

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36

rahul ·2011-03-05 09:39:21

1² -2² +3² -4² + ...... +99²-100²

Too easy....

a² - b² = (a + b)(a - b), kills this question

Let, A = 1² -2² +3² -4² + ...... +99²-100²

so, A = (1 + 2)(1 - 2) + (3 + 4)(3 - 4) + ...... + (99 - 100)(99 + 100)
= - (3 + 7 + 11 + ...................... + 199)

clearly, 3,7,11,..... 199 is in A.P

where, a = 3 , d = 4 , l = 199
so, let there be n terms in the A.P

so, a + (n - 1)d = 199
=> 3 + (n - 1)(4) = 199
=> 3 + 4n - 4 = 199
=> 4n - 1 = 199
=> 4n = 200
=> n = 50

so, S₅₀ = 50/2 [a + l] = 25 (3 + 199) = 25 x 202 = 5050

so, 5050 is the required answer

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