শিক্ষা

Arithmetic Progression   a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d   d =  a 2 – a 1 = a 3 – a 2 = ……. = a n – a n – 1   nth Term of an AP :-   a n = a + (n − 1) × d Sum of N Terms of AP:-     S n = n/2[2a + (n − 1) × d] Sum of AP when the Last Term is Given :-     S  = n/2 (first term + last term)   Geometric Progression   a, ar, ar 2 , ar 3 , ar 4 ,…, ar n-1 Nth Term of G.P:-    a n  = t n = ar n-1 Sum of N term of GP:-   S n = a[(r n  – 1)/(r – 1)] if r ≠ 1 and r > 1   S n = na if r = 1 S n = a[(r n  – 1)/(r – 1)] if r ≠ 1 and r > 1     Harmonic progression  

Hyperbolic Trigometry Hyperbolic sine: Hyperbolic cosine: Hyperbolic tangent: Hyperbolic cotangent: Hyperbolic secant: Hyperbolic cosecant:

Sigma Notation:-   Pi Notation:- Intersection Notation:-   Union Notation:-

Algebra 2 3 =8; 3 3 =9; 4 3 =64; 5 3 =125; 6 3 =216; 7 3 =343; 8 3 =512; 9 3 =729; 10 3 =1000 (a+b) 2 =a 2 +2ab+b 2   (a-b) 2 =a 2 -2ab+b 2    (a+b) 2 =(a-b) 2 +4ab    (a-b) 2 =(a+b) 2 -4ab     a 2 +b 2 =(a-b) 2 +2ab   a 2 +b 2 =(a+b) 2 -2ab    a 2 -b 2 =(a+b)(a-b)    2(a 2 +b 2 )=(a+b) 2 +(a-b) 2   ab=((a+b)/2) 2 -((a-b)/2) 2   (a+b) 3 =a 3 +3a 2 b+3ab 2 +b 3 (a-b) 3 =a 3 -3ab 2 +3ab 2 -b 3 (a+b) 3 =a 3 +b 3 +3ab(a+b) (a-b) 3 =a 3 -b 3 -3ab(a-b) a 3 +b 3 =(a+b) 3 -3ab(a+b) a 3 +b 3 =(a+b)(a 2 -ab+b 2 ) a 3 -b 3 =(a-b) 3 +3ab(a-b) a 3 -b 3 =(a-b)(a 2 +ab+b 2 ) (a+b+c) 2 =a 2 +b 2 +c 2 +2(ab+bc+ca) a 2 +b 2 +c 2 =(a+b+c) 2 -2(ab+bc+ca) ab+bc+ca=((a+b+c) 2 -(a 2 +b 2 +c 2 ))/2 4ab=(a+b) 2 -(a-b) 2