Script for Useful maths formula for competitive exam

Useful maths formula for competitive exam

Algebra:

● Laws of Indices:

(i) a^m ∙ aⁿ = a^{m + n}

(ii) a^m/aⁿ

(iii) (a^m)ⁿ = a^mn

(iv) a⁰ = 1 (a ≠ 0).

(v) a^{- n} = 1/aⁿ

(vi) ⁿ√a^m = a^m/n

(vii) (ab)^m = a^m ∙ bⁿ.

(viii) (a/b) ^m = a^m/bⁿ

(ix) If a^m = b^m (m ≠ 0), then a = b.

(x) If a^m = aⁿ then m = n.

● Arithmetical Progression (A.P.):

(i) The general form of an A. P. is a, a + d, a + 2d, a+3d,.....

where a is the first term and d, the common difference of the A.P.

(ii) The nth term of the above A.P. is t_n = a + (n - 1)d.

(iii) The sum of first n terns of the above A.P. is s = n/2 (a + l) = (No. of terms/2)[1st term + last term] or, S = ⁿ/₂ [2a + (n - 1) d]

(iv) The arithmetic means between two given numbers a and b is (a + b)/2.

(v) 1 + 2 + 3 + ...... + n = [n(n + 1)]/2.

(vi) 1² + 2² + 3² +……………. + n² = [n(n+ 1)(2n+ 1)]/6.

(vii) 1³ + 2³ + 3³ + . . . . + n³ = [{n(n + 1)}/2 ]².

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