Some important formulae

Formulae:-

1. 1+2 +3+4+...........n=n(n+1)/2.

Ex:-1+2+3+4+5+6+7+8=8(8+1)/2=36

2. 2+4+6+8+..........n terms=n(n+1)

Ex:-2+4+6+8+10+12+14=7(7+1)=56.

3. 1+3+5+7+..........n terms=n²

Ex-1+3+5+7+9+11+13+15+17=9²⁼81

Tricky method(square of numbers)

Square of numbers:-

 

    ( a)⇒        21²=20²+1(20+21)=441

                      22²=20²+2(20+22)=484

                      23²=20²+3(20+23)=529

    (b)⇒         29²=30²-1(29+30)=841

                      28²=30²-2(28+30)=784

   (c)⇒           71²=70²+1(70+71)=5041

                       72²=70²+2(70+72)=5184

   (d)⇒            79²=80²-1(79+80)=6241

                        78²=80²-2(78+80)=6084

 Note-This trick is valid for any digits number