ICSE Class 10 Answered
What is the sum of n terms of a series whose mth term is 2^m + 2m?
Asked by dwivedi_anand | 09 Nov, 2018, 11:53: AM
Expert Answer
Given
tm = 2m + 2m
∴tn = 2n +2n
sum of n terms = ∑tn=∑(2n +2n)
=∑2n + ∑2n
make it two parts
i) ∑2n = [2+2²+2³+..........+2n]series is GP
here first term =a =2
common ratio =r = t2/t1 = 2²/2 = 2 >1
sum of n terms in GP = a(rn -1)/(r-1)
= [2(2n -1)]/(2-1)
= [2(2n -1)]/(2-1)
=2(2n -1)------(1)
ii) sum of n terms =∑ 2n = 2∑n=2[1+2+3+....+n]
=2n(n+1)/2 since sum of n natural numbers = n(n+1)/2
ii) sum of n terms =∑ 2n = 2∑n=2[1+2+3+....+n]
=2n(n+1)/2 since sum of n natural numbers = n(n+1)/2
=n(n+1)------(2)
therefore
∑tn sum of n terms in given series = (1) +(2)
= 2(2n - 1) +n(n+1)
∑tn sum of n terms in given series = (1) +(2)
= 2(2n - 1) +n(n+1)
Answered by Arun | 09 Nov, 2018, 01:50: PM
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