Page 30 - Math Grade 11 (Advance)

PROEUS DARA

t~'i§jLfUlli5'i5qJ:lrhh P(n) rJg)tJtm::UiU n EIN* tf!iUJ~
u

0 ' 0 ' 1
rumHH1a 1 Lnnruuqp fHu'i§filCll X 2 + 2 X 3 + 3 X 4 + ... + n X (n + 1) = 3n(n + 1 )(n + 2)
nncrtm::Lf!iU n EIN* tttl rutLli1mHH~'i:flS~Yf!irulg)l9Jl

0
mm:: n = I
1
»b~l:Htitl I X 2 = 2 Hb~tlnn -3 X 1 x(l + 1)(1 +2) = 2
Fl 4
Fl "'

.. 0
!a'i5'i:f1Gl nJYfilClClg)utm:: n = k tf!iQ1S
1
lx2+2x3+3x4+ ... +kx(k+l) = }k(k+l)(k+2) (k=l, 2, 3, ... )

'UblmG'lnJYfilCltlg)tJtm:: n = k sl§'iQ1ShlYfilCltlg)tJ&mg n = k+ 1
Ul " u
1
1x2+2x3+3x4+ ... +k(k+l)+(k+l)(k+2) = }(k+l)(k+2)(k+3)
1
tf!i'i:flS lx2+2x3+3x4+ ... +kx(k+l) = k(k+l)(k+2)
3
eJ QJ OQ1'::1 Ql
tOY (k+ l)(k+2) tillHtl!tlbClHShlYffU tf!iQ1S
Fl
1
1 X 2 + 2 X 3 + 3 X 4 + ... + k X ( k + 1 ) + ( k + 1 ) ( k + 2) = 3 k( k + 1) ( k + 2) + ( k + 1) ( k + 2)
3
= (k+l)(k+2)Gk+l) = (k+I)(k+2)(k; )

= ~(k+ l)(k+2)(k+3) rJg)

~msg n5YfilCltlncrtm8UiU nEIN*

~crtSl: lx2+2x3+3x4+ ... +nx(n+l) = ~n(n+l)(n+2)(n=1, 2, 3, ... )

25