`4+8+12+.....+4n=2n(n+1)`

lim_ (n rarr oo) (1.2 + 2.3 + 3.4 + .... + n (n + 1)) / (n ^ (3))

Prove by PMI that 1.2+2.3+3.4+....+n(n+1)=((n)(n+1)(n+2))/(3),AA n in N

Prove that 2.4.6.8..........2n<(n+1)^(n)*(n in N)

lim_(n->oo) (1.2+2.3+3.4+....+n(n+1))/n^3

lim_(n rarr oo) (1.2 +2.3+3.4+ .....+n(n+1))/n^(3)=

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(0)+4C_(1)+8C_(2)+12C_(3)+......+4nC_(n)=1+n.2^(n+1)

Sum of n terms of series 12+16+24+40+.... (A) 2(2^n -1)+8n (B) 2(2^n-1)+6n (C) 3(2^n-1)+8n (D) 4(2^n-1)+8n

Find the indicated terms in each of the following sequences whose nth terms are: a_n=5_n-4; a_(12) and a_(15) a_n=(3n-2)/(4n+5); a_7 and a_8 a_n=n(n-1); a_5 and a_8 a_n=(n-1)(2-n)(3+n); a_1,a_2,a_3 a_n=(-1)^nn ; a_3,a_5, a_8

Prove that for n=1, 2, 3... [(n+1)/2]+[(n+2)/4]+[(n+4)/8]+[(n+8)/16]+...=n where [x] represents Greatest Integer Function