Question

sum
the series
3x12+5*247x32+ ....n term​

Answer 1

Step-by-step explanation:

Case (I): Sum when there are n terms in series

The series is 1+2+3+4+……

The series is an A.P. Therefore,

Its sum up to n terms is given by the formula,

Sum = (n/2){2a + (n-1)d} …………………………………………(1)

where a= the first term and d = common difference. d is found by subtracting any term from the term which follows it

In the problem a=1 and from the definition of common difference, d=2–1=3–2=1.

Substituting for a and d in (1),

Sum=(n/2){2.1 + (n-1)1} = (n/2)(2+n-1)=(n/2)(n+1)

Or, Sum=n(n+1)/2

Taking the first four terms (1,2,3,4) of the series, n=4 and

The sum = 4(4+1)/2 = 4x5/2= 10

Case (II): Series is infinite

Here, the terms of the series go on increasing within limit. So the sum is also infinite.

PLEASE LOOK AT THAT