Math Editor

Sequence & series

Arithmetic series

1.n th term =a+(n-1)d (arithmetic)

2.Σ of n th term =n/2{2a+(n-1)d}

3.Σ of n th term =n/2(a+p)

4.n=(p-a)/d+1

5.1+2+3+...+n=n(n+1)/2

6.1²+2²+3²+...+n²=n{(n+1)(2n+1]}/6

7.1³+2³+3³+...n³=[n(n+1)/2]²

8.1+3+5+...+n=n²

9.2+4+6+...+n=n(n+1)

→2b=a+c

→b=(a+c)/2

∞=infinity

Σ=summation

r=common ratio

Geometric series

1.n th term=arⁿ⁻¹

2.Σ of n th term=a(rⁿ -1)/r-1 [r>1]

3.Σ of n th term=a(1-rⁿ )/1-r [r<1]

4.Σ of n th term=a/1-r [r=∞]

5.Σ of n th term=an [r=1]

6.a+b+c+d+... Then,a/b=b/c

→b²=ac