sigma with pie [part -4]

Algebra Level 2

∑ k = 1 100 k − ∏ k = 1 7 k = ? \displaystyle\sum^{100}_{k=1} k - \displaystyle\prod^{7}_{k=1} k= ?


The answer is 10.

Sudoku Subbu by sudoku subbu , 19, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Sudoku Subbu
Jan 18, 2015

∑ k = 1 100 = 100 ( 100 + 1 ) 2 = 100 ( 101 ) 2 = 50 × 101 = 5050 \displaystyle\sum^{100}_{k=1}=\frac{100(100+1)}{2}=\frac{100(101)}{2}=50\times101 = 5050 . ∏ k = 1 7 = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 7 ! = 5040 \displaystyle\prod^{7}_{k=1}=1\times2\times3\times4\times5\times6\times7=7!=5040 therefore ∑ k = 1 100 − ∏ k = 1 7 = 5050 − 5040 = 10 \displaystyle\sum^{100}_{k=1} - \displaystyle\prod^{7}_{k=1}=5050-5040=10

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Nothing like ∑ k = 1 100 \displaystyle\sum_{k=1}^{100} actually exist. You missed a "k" after summation. It must be like ∑ k = 1 100 k \displaystyle\sum_{k=1}^{100} k

(Similarly with continued product)

Pranjal Jain - 6 years, 4 months ago

Log in to reply

ok thanks i changed it

sudoku subbu - 6 years, 4 months ago

Log in to reply

In your solution as well?

Pranjal Jain - 6 years, 4 months ago

Log in to reply

@Pranjal Jain – let it be while how is my problem ha interesting naa?

sudoku subbu - 6 years, 4 months ago

  • Use \displaystyle\sum for ∑ \displaystyle\sum

  • Use \displaystyle\prod for ∏ \displaystyle\prod

    • It looks better!

    Pranjal Jain - 6 years, 4 months ago
    Kartik Kulkarni
    Feb 1, 2015

    We can also say

    ∑ k = 1 100 k \sum_{k=1}^{100} k = 1 + 2 + 3 ... +100

    = 1+100+2+199...

    =101+101...(50 times )

    =5050

    & ∏ k = 1 7 k \prod_{k=1}^{7} k = 7! =5040

    therefore 5050 - 5040 = 10 \boxed{10}

    0 Helpful 0 Interesting 0 Brilliant 0 Confused
    Chew-Seong Cheong
    Jan 21, 2015

    ∑ k = 1 100 k − ∏ k = 1 7 k = 100 ( 100 + 1 ) 2 − 7 ! = 5050 − 5040 = 10 \displaystyle \sum _{k=1} ^{100} {k} - \prod _{k=1} ^7 {k} = \frac {100(100+1)}{2} - 7! = 5050 - 5040 = \boxed{10}

    0 Helpful 0 Interesting 0 Brilliant 0 Confused

    0 pending reports

    ×

    Problem Loading...

    Note Loading...

    Set Loading...