I just started to do some maths because it is going to be my last year and I met this problem:
2 · 4 - 4 · 6 + 6 · 8 - 8· 10 + ... + 98 · 100 - 100 · 102 =?
I completely forgot how to solve these. Could anyone remind me?
2 * 4 - 4 * 6 + 6 * 8 - 8* 10 + 10*12 - 12*14 + 14*16 - 16*18 ... + 98 · 100 - 100 · 102
= [ 2 * 4 - 4 * 6 ]+ [6 * 8 - 8* 10] + [10*12 - 12*14] + [14*16 - 16*18] ... + [98 · 100 - 100 · 102]
= 4*(-4) + 8*(-4) + 12*(-4) .... 100*(-4)
= (-16)*[1 + 2 + 3 + 4 + ....+23 + 24 + 25]
= (-16) * 25 * 26/2
= - 5200
Hi I just came back from holiday. I understand everything except where you get 25 *26/2 after (-16) .
Compare with the statement made in the line above.
What does it equate to?
Do you know the expression for the series = 1 + 2 + 3 + 4 ..... +(n-2) + (n-1) + n ?
Elaborate please. I can't see anything special in the line above.
It seems like no. Could you remind me and I will finish.
Maybe I understood.
{1 + 2 + 3 + ,,, + 25}
Brackets are arithmetic progression I think. Because d = 1 .
I can write it in S(25)=a1+a25/2 *25 ? Then I get 1 + 25/2 * 25 = 13 * 25 = 325
325 * (-16) = -5200 ! OK?