" 4."4^(3)+8^(3)+12^(3)+cdots" upto "n" terms "=16n^(2)(n+1)^(2)" ."

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

Using the principle of M.I, prove that 4^3+8^3+12^3 + ……… n terms = 16n^2(n+1)^2

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

(1-1/n) + (1 - 2/n) + (1 - 3/n)+ …… upto n terms = ?

If (1.2+2.3+3.4+cdots "to n terms")/(1+2+3+cdots "to n terms") =6 find n.

Find the sum, (i) 4-(1)/(n)+4-(2)/(n)+4-(3)/(n) …………upto n terms (ii) 1+(-2)+(-5)+….+(-236) .

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) .

Find the sum up to n terms :n.1+(n-1).2+(n-2)3+(n-3).4+....