Test:1 QNo:3

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

club the terms like

1²-2²=(1+2)(1-2)

1²-2² = -3
3²-4² = -7
5²-6² = -11

So u get an AP of 50 terms :-)

or u can use summation series

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