Problem solution

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Shad
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Joined:Tue Dec 22, 2020 9:46 pm
Location:Jamalpur
Problem solution

Unread post by Shad » Sun Dec 27, 2020 7:40 pm

২,৫,১০,১৭,২৬,৩৭................ ধারাটির ১০০ তম পদ কত হবে।


দয়া করে নিয়মটা বলে দিবেন।

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Mehrab4226
Posts:230
Joined:Sat Jan 11, 2020 1:38 pm
Location:Dhaka, Bangladesh

Re: Problem solution

Unread post by Mehrab4226 » Mon Dec 28, 2020 7:21 pm

$5-2=3$
$10-5=5$
$17-10=7$
$26-17=9$
$37-26=11$

First-term $= 2$
2nd term $= 2+(3)$
3rd term $= 2+(3+5)$
4th term $= 2+(3+5+7)$
.
.
100th term$= 2+(3+5+7 +\cdots \text{99 odd numbers})$

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We know,
$1+3+5+ \cdots 2n-1=n^2$
$\therefore 3+5+9+ \cdots 99 terms= n^2-1[n=100]$[Why? Think finding it out as an exercise]
$\therefore$ 100th term $= 2+(100)^2-1$
$=1+10000$
$=10001$
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré

@muzahid_emon
Posts:1
Joined:Thu Feb 04, 2021 11:27 am

Re: Problem solution

Unread post by @muzahid_emon » Thu Feb 04, 2021 11:36 am

এই ধারার n তম পদ হচ্ছে n ²+1
১ম পদ = 1²+1 =2
২য় পদ = 2²+1 =5
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এখন , ধারাটির 100 তম পদ = 100²+1 = 10001

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