Question

The sum to n terms of the series 1 + (1 + 3) + (1 + 3 +5 )+ ...... is ?

Please show the process also....!

Answer 1

we will divide into 3 APs

(1).  1 (only single term) upto n terms...
=> sum = n

(2)      3 (only single term) upto  (n-1) terms
=> sum= ($\frac{n-1}{2}$)*2(3)+(n-1-1)0               (d=0)
             = ($\frac{n-1}{2}$)6

(3)    5 (only one term) upto (n-2 ) terms
=>sum =  ($\frac{n-2}{2}$)*2(5)                           (d=0)
             = ($\frac{n-2}{2}$)*10

summing up all the APs

=> n+ (n-1)/2*6 +(n-2)/2*10
=>n+ 3(n-1)+5(n-2)
=>n+3n-3+5n-10
=.9n-13