Algebra - summation

62

Lokesh Verma ·2010-04-30 01:14:32

Hint: 1=2-1

2=3-1

3 = 4-1

Now try..

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ut10 ·2010-04-30 01:20:12

thanks bhaiya.
2 : 1⁴+2⁴+3⁴+4⁴+.......

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62

Lokesh Verma ·2010-04-30 01:23:24

2nd one the first proof is quite boring...

It goes like this:

1⁵-0⁵ = 1⁴
2⁵-1⁵ = 2⁴+2³+2²+2+1
3⁵-2⁵ = 3⁴+2.3³+2²3²+....

....

...

Then add..

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student ·2010-04-30 01:42:12

apply direct summation

n(n+1)²=n(n²+2n+1)

Î£n³+2Î£n²+Î£n

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62

Lokesh Verma ·2010-04-30 01:43:29

how does that help? I din get ur proof RPF?

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student ·2010-04-30 01:45:57

second one same as bhaiya

Î£(n⁵-(n-1)⁵)+10Î£n³-10Î£n²+5Î£n-15=Î£n⁴

Î£n⁴=(n⁵)+10Î£n³-10Î£n²+5Î£n-15

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Sridhar M ·2010-04-30 01:46:48

He found the nth term and the resulting summation is found.

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student ·2010-04-30 01:47:42

i think bhaiya thought i posted solution for second one

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ut10 ·2010-04-30 07:44:44

find the sum of the series 12 ,40 ,90 ,168 ,280 ,432,.................

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62

Lokesh Verma ·2010-04-30 07:50:24

See these:

2x6
4.10
6. 15
8. 21
10.28
12.36

Now try.

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ut10 ·2010-04-30 08:00:49

thanks bhaiya gr8
getting Tn= 2n * (n²+5n+6)/2
by multiplying and then doing summation getting right solution.

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