Using Mathematical induction. For all `n in N`. Show that
`a+(a+d)+(a+2d)+…………..n "upto n terms" = n/2 [2a+(n-1)d]`.

2+ 3.2 + 4.2^(2) + …... upto n terms =

1^(2) + 3^(2) + 5^(2) + …. upto n terms =

Using the principle of finite Mathematical Induction prove the following: (vi) 2+3.2+4.2^(2)+………."upto n terms" = n.2^(n) .

Prove that a+(a+d)+(a+2d)+........n "terms"=n/2(2a+(n-1)d)

Using Mathematical Induction, prove that statement for all n in N 1.2.3+2,3,4+……….+("upto n terms")=(n(n+1)(n+2)(n+3))/(4) .

Using the principle of finite Mathematical Indcution prove that 2.3 + 3.4 + 4.5 + ……."upto n terms" = (n(n^(2)+6n+11))/(3) .

Using the principle of finite Mathematical Induction prove the following: (iii) 1/(1.4) + 1/4.7 + 1/7.10 + ……… + "n terms" = n/(3n+1) .

2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

Use mathematical induction to prove that 2 n - 3 le 2^(n-2) for all n ge 5, n in N