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Fill in the blank so that the following equations are true: m Ση=0 i=1 100 Σ2 = 0 i=3

Fill in the blank so that the following equations are true: m Ση=0 i=1 100 Σ2 = 0 i=3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Fill in the blank so that the following equations are true
Fill in the blank so that the following equations are true: η Ση=0 i=1 100 Σ2% = 0 i=3
Transcribed Image Text:Fill in the blank so that the following equations are true: η Ση=0 i=1 100 Σ2% = 0 i=3
Expert Solution
Step 1

Given series is

∑i=1nn

Expanding, we get

∑i=1nn=1+2+3+...+n

The above series is arithmetic series with n number and its common difference is d=1

Since sum of arithmetic series is

Sn=n22a+(n-1)d

where a is the first element.

We have a=1

So we have

Sn=n22+(n-1)⇒Sn=n2(n+1)

Hence we can say

∑i=1nn=n(n+1)2

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